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CBSE Worksheets for Class 11 Maths

CBSE Worksheets for Class 11 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 11 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 11 Maths Worksheets for the students of Class 11. All our CBSE NCERT Class 11 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 11 Maths will be useful to test your conceptual understanding.

Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 11 Maths Number of Worksheets: 42

CBSE Class 11 Maths Worksheets PDF

All the CBSE Worksheets for Class 11 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 11 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 11 Maths Worksheet. CBSE Worksheets for Class 11 Math can also use like assignments for Class 11 Maths students.

Binomial Theorem

• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 1
• CBSE Worksheets for Class 11 Mathematics Binomial Theorem Assignment 2

Complex Numbers and Quadratic Equation

• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 1
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 2
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 3
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 4
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 5
• CBSE Worksheets for Class 11 Mathematics Complex Numbers and Quadratic Equation Assignment 6

Conic Sections

• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 1
• CBSE Worksheets for Class 11 Mathematics Conic Sections Assignment 2

Introduction To 3Dimensional Geometry

• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 1
• CBSE Worksheets for Class 11 Mathematics Introduction To 3Dimensional Geometry Assignment 2

Linear Inequalities

• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 1
• CBSE Worksheets for Class 11 Mathematics Linear Inequalities Assignment 2

Permutations and Combinations

• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 1
• CBSE Worksheets for Class 11 Mathematics Permutations and Combinations Assignment 2

Principle of Mathematical Induction

• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 1
• CBSE Worksheets for Class 11 Mathematics Principle of Mathematical Induction Assignment 2

Probability

• CBSE Worksheets for Class 11 Mathematics Probability Assignment 1
• CBSE Worksheets for Class 11 Mathematics Probability Assignment 2

Relations and Functions

• CBSE Worksheets for Class 11 Mathematics Relations and Functions Assignment

Sequences and Series

• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 4
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 5
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 6
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 7
• CBSE Worksheets for Class 11 Mathematics Sequences and Series Assignment 8
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 1
• CBSE Worksheets for Class 11 Mathematics Set Theory Assignment 2
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 1
• CBSE Worksheets for Class 11 Mathematics Statistics Assignment 2

Straight Lines

• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 1
• CBSE Worksheets for Class 11 Mathematics Straight Lines Assignment 2

Trigonometric Ratios

• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 1
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 2
• CBSE Worksheets for Class 11 Mathematics Trigonometric Ratios Assignment 3
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 1
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 2
• CBSE Worksheets for Class 11 Mathematics Sample Paper 2014 Assignment 3
• CBSE Worksheets for Class 11 Mathematics Mathematical Reasoning Assignment

Advantages of CBSE Class 11 Maths Worksheets

• By practising NCERT CBSE Class 11 Maths Worksheet , students can improve their problem solving skills.
• Helps to develop the subject knowledge in a simple, fun and interactive way.
• No need for tuition or attend extra classes if students practise on worksheets daily.
• Working on CBSE worksheets are time-saving.
• Helps students to promote hands-on learning.
• One of the helpful resources used in classroom revision.
• CBSE Class 11 Maths Workbook Helps to improve subject-knowledge.
• CBSE Class 11 Math Worksheets encourages classroom activities.

Worksheets of CBSE Class 11 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 11 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 11 Maths Worksheets PDF .

Now that you are provided all the necessary information regarding CBSE Class 11 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 11 Math revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus.  Working on CBSE Class 11 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 11 Math Worksheets to secure good score.

CBSE Worksheets For Class 11

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Important Questions for CBSE Class 11 Maths (2024-25)

• Class 11 Important Question

CBSE Class 11 Maths Chapter wise Important Questions - Free PDF Download

One of the most important subjects that students attempt in the science stream is Mathematics. For those taking exams in their eleventh grade, having the important questions for class 11 maths beforehand can help prepare better. We at Vedantu provide you with the opportunity to gain a lot of advantages when it comes to studying before the exam:

We provide the important questions for class 11 maths laid out chapter wise with solutions. Students can accordingly set their schedule

All the questions for the examination are available in a free PDF download any time of the year so you can choose when you want to include it in your study schedule

The questions are all prepared in the latest CBSE syllabus of the latest year of the CBSE board and are updated every annual academic year

Solving these questions will give students the advantage of preparing themselves better before their class 11 examinations

The NCERT important questions for class 11 Maths with answers are present for all chapters from Sets to Probability

There are a whole host of other advantages that come when you want to download the class 11 Maths NCERT important questions available as a free PDF download

Download CBSE Class 11 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 11 Maths Important Questions for All chapters:

Chapter wise Important Questions for CBSE Class 11 Maths

Important Questions for Class 11 Maths CBSE Board

There are a lot of advantages that come with our different services for education. We provide private tutors for students that will help them understand the important questions for class 11 Maths that come chapter wise with free PDF solutions better. Here, they can solve problems at their own pace and also clear their doubts with the tutor online.

Our tutors are experienced and will be able to streamline themselves to the student's schedule. Students can also decide a schedule that works for them so that they can study at a pace that suits them. Our teachers will be able to guide you better when it comes to how you must pace your answers, tackling the right questions and practising well so you can perform better.

CBSE Class 11 Maths Weightage 2024-25

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At Vedantu, you will be able to also tap into various that we can provide to you such as CBSE Important question papers , revision notes , CBSE syllabus and so much more.

Students must enjoy their studies, and we want to help them understand their lessons better instead of just studying by rote.

We provide students with personal teachers for subjects such as Maths, Physics, Chemistry and Biology . They know exactly what sort of questions appear in exams due to their vast years of experience and this can be very helpful for students who are slow learners.

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Other CBSE Class 11 Important Questions Links

Important Related Links for CBSE Class 11

FAQs on Important Questions for CBSE Class 11 Maths (2024-25)

Q 1: How Vedantu’s answers assist us in scoring good marks in the exam?

All our solutions are framed with the aid of our subject matter specialists of maths and that they have given every part of the bankruptcy at the side of the exercise questions which might be referred to at the give up of the bankruptcy. Our Solutions for Class 11 Maths will provide an explanation for to you all the essential major points of the chapter. This will basically help you in building up a sturdy basis of the challenge and eventually you can also enhance your grades with it. The answers supplied through us will help in revision before the examination. These paintings as last-minute have a look at notes for your exam which could be visible just earlier than the examination to memorise all the key factors.

Q 2: What are the important concepts in chapter 11 conic sections?

The chapter covers topics like parts of a cone which teaches about circle, ellipse, parabola, hyperbola and degenerate conic sections . You will also learn about Relationship between the semi-major axis, semi-minor axis and the distance of the focus from the centre of the ellipse, Standard equations of an ellipse, Standard equations of a parabola and Special cases of an ellipse .

The chapter also discusses on Eccentricity, Latus rectum, Standard equation of Hyperbola and minor axis of the distance . This is one of the important chapters of class 11 maths which also explains about the equilateral triangle and equations of the hyperbola.

Q 3: What are the principal topics in relation and functions?

The chapter introduces you to the relations and features. You will particularly encounter the Cartesian Product of Sets and Relations . Here, you may, in particular, realize approximately the real-life model of cartesian products which are explained with the assist of Lindt chocolates are available in 5 shapes, three flavours and in six colours.

You can also be taught of functions which encompass Some capabilities and their graphs along with Identity feature, Constant function, Polynomial feature, Rational features, The Modulus function, Signum feature and Greatest integer characteristic. You will also study about the Algebra of real functions which incorporates Addition of two actual features, Subtraction of a real character from another, Multiplication with the aid of a scalar, Multiplication of two real capabilities and The quotient of two real capabilities.

Q 4: What will I learn in chapter four Mathematical Induction?

Mathematical Induction is a specific technique that is primarily used to prove a given statement or a theorem. The important section of this method is that the theorem should always be true for every natural number given. It is one of the useful methods as you do not have to solve an equation or a statement for every possible value it could take.

You will get familiar with the following pointers while studying Mathematical Induction:

Proving the given illustration or statement is the primary motive.

The proof should always stand true for all the values consisting of natural numbers.

The statement should be true for the initial value as well.

The statement should be true for all other values till nth iteration.

Every step involved in the proof must be justified and has to be true.

Q5. Name the important concepts discussed in Chapter 11 Conic Sections of NCERT Solutions for Class 11 Maths.

Chapter 11 "Conic Sections" deals with various conic sections like circles, ellipses, parabolas, and hyperbolas. The important topics of this chapter are as follows:

a) Sections of a cone

b) Circles

c) Ellipses

d) Special cases of an ellipse

e) Parabolas

f) Standard equations of a parabola

g) Hyperbolas

h) Degenerated Conic Sections

i) Latus rectum

j) Eccentricity 

k) Standard equation of an ellipse

Important questions on all these topics are available here.

These solutions are available on Vedantu's official website( vedantu.com ) and mobile app free of cost.

Q6. What are the main topics covered in important questions of “Relations and Functions” for Class 11 Maths?

"Relations and Functions" is Chapter 2 in the NCERT textbook for Class 11. This is an important chapter and includes the following topics:

Cartesian products of sets

Functions and their graphs

   i) Identity function

            ii) Polynomial function

            iii) Constant function

            iv) Rational function

            v) Modulus function

            vi) Signum function

            vii) Greatest integer function

Algebra of real functions

Students can find all the important questions from this chapter here.

Q7. Which book is best for Class 11 Maths?

Ans: The most important book for Class 11 Mathematics is the main NCERT textbook. Almost all questions in the CBSE exam are directly asked from the NCERT textbook. For this very reason, it is extremely important to understand the concepts mentioned in the NCERT textbook well and practice the NCERT example, and practice questions thoroughly.

Apart from this, students can also practice Vedantu's important questions, NCERT Solutions, sample papers, and previous years' question papers for thorough practice.

Q8 . How many chapters are there in Class 11 Maths?

Ans:   Class 11 CBSE Maths curriculum consists of a total of 16 chapters.  Vedantu has carefully enlisted the important questions from all these chapters. Vedantu's Important Questions for Class 11 Mathematics will allow the students to practice questions that are significant from the exam point of view. It will also teach them the right way to compose step-by-step answers to these questions so they do not lose important marks in exams due to incomplete answers.

Q9. Is Class 11 Maths tough?

Ans: Class 11 Mathematics is definitely not a child's play. It has some complicated topics as well. However, this does not mean that with proper guidance, planning, and effort you cannot ace this subject. You can even top in Class 11 Maths if you follow the following steps:

a) Understand and practice NCERT Solutions and example questions thoroughly.

b) Refer to Vedantu's Important questions and practice

c) Solve loads of sample papers and previous years' question papers.

d) Practice over and over again.

Important Questions for CBSE Class 11

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Chapter 3 Class 11 Trigonometric Functions

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NCERT Solutions of Chapter 3 Class 11 Trigonometry is available free at teachoo. You can check the detailed explanation of all questions of exercises, examples and miscellaneous by clicking on the Exercise link below.

We had learned Basics of Trigonometry in Class 10. In this chapter, we will learn

• What is a positive or a negative angle
• Measuring angles in Degree , Minutes and Seconds
• Radian measure of an angle
• Converting Degree to Radians , and vice-versa
• Sign of sin, cos, tan in all 4 quadrants
• Finding values of trigonometric functions when one value is given (Example: Finding value of sin, cot, cosec, tan, sec, when cos x = -3/5 is given)
• Finding Value of trigonometric functions, given angle
• Solving questions by formula like  (x + y) formula, 2x 3x formula, Cos x + cos y formula , 2 sin x sin y formula 
• Finding principal and general solutions of a trigonometric equation
• Sin and Cosine Formula with supplementary Questions

Important questions are marked, and Formula sheet is also provided. Click on an exercise or topic to begin.

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NCERT Solutions for Class 11 Maths Chapter 1 – Sets

Ncert solutions for class 11 maths chapter 1 – sets pdf.

Free PDF of NCERT Solutions for Class 11 Maths Chapter 1 – Sets includes all the questions provided in NCERT Books prepared by Mathematics expert teachers as per CBSE NCERT guidelines from Mathongo.com. To download our free pdf of Chapter 1 – Sets Maths NCERT Solutions for Class 11 to help you to score more marks in your board exams and as well as competitive exams.

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Class 11 Mathematics Trigonometry Assignments

We have provided below free printable Class 11 Mathematics Trigonometry Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 11 Mathematics Trigonometry . These Assignments for Grade 11 Mathematics Trigonometry cover all important topics which can come in your standard 11 tests and examinations. Free printable Assignments for CBSE Class 11 Mathematics Trigonometry , school and class assignments, and practice test papers have been designed by our highly experienced class 11 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Trigonometry Class 11 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Trigonometry Class 11. Students can click on the links below and download all Pdf Assignments for Mathematics Trigonometry class 11 for free. All latest Kendriya Vidyalaya Class 11 Mathematics Trigonometry Assignments with Answers and test papers are given below.

Mathematics Trigonometry Class 11 Assignments Pdf Download

We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 11 Mathematics Trigonometry . Students and teachers can download and save all free Mathematics Trigonometry assignments in Pdf for grade 11th. Our expert faculty have covered Class 11 important questions and answers for Mathematics Trigonometry as per the latest syllabus for the current academic year. All test papers and question banks for Class 11 Mathematics Trigonometry and CBSE Assignments for Mathematics Trigonometry Class 11 will be really helpful for standard 11th students to prepare for the class tests and school examinations. Class 11th students can easily free download in Pdf all printable practice worksheets given below.

Topicwise Assignments for Class 11 Mathematics Trigonometry Download in Pdf

Advantages of Class 11 Mathematics Trigonometry Assignments

• As we have the best and largest collection of Mathematics Trigonometry assignments for Grade 11, you will be able to easily get full list of solved important questions which can come in your examinations.
• Students will be able to go through all important and critical topics given in your CBSE Mathematics Trigonometry textbooks for Class 11 .
• All Mathematics Trigonometry assignments for Class 11 have been designed with answers. Students should solve them yourself and then compare with the solutions provided by us.
• Class 11 Students studying in per CBSE, NCERT and KVS schools will be able to free download all Mathematics Trigonometry chapter wise worksheets and assignments for free in Pdf
• Class 11 Mathematics Trigonometry question bank will help to improve subject understanding which will help to get better rank in exams

Frequently Asked Questions by Class 11 Mathematics Trigonometry students

At https://www.cbsencertsolutions.com, we have provided the biggest database of free assignments for Mathematics Trigonometry Class 11 which you can download in Pdf

We provide here Standard 11 Mathematics Trigonometry chapter-wise assignments which can be easily downloaded in Pdf format for free.

You can click on the links above and get assignments for Mathematics Trigonometry in Grade 11, all topic-wise question banks with solutions have been provided here. You can click on the links to download in Pdf.

We have provided here topic-wise Mathematics Trigonometry Grade 11 question banks, revision notes and questions for all difficult topics, and other study material.

We have provided the best collection of question bank and practice tests for Class 11 for all subjects. You can download them all and use them offline without the internet.

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NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions

September 22, 2019 by phani

Get Free NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1, Ex 3.2, Ex 3.3, Ex 3.4, and Miscellaneous Exercise PDF in Hindi and English Medium. Trigonometric Functions Class 11 Maths NCERT Solutions are extremely helpful while doing your homework. Trigonometric Functions All Exercises Class 11 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers.

Class 11 Maths Trigonometric Functions NCERT Solutions in English Medium and Hindi Medium

• Trigonometric Functions Class 11 Ex 3.1
• Trigonometric Functions Class 11 Ex 3.2
• Trigonometric Functions Class 11 Ex 3.3
• Trigonometric Functions Class 11 Ex 3.4
• Trigonometric Functions Class 11 Miscellaneous Exercise

त्रिकोणमितीय फलन प्रश्नावली 3.1 का हल हिंदी में

• त्रिकोणमितीय फलन प्रश्नावली 3.2 का हल हिंदी में
• त्रिकोणमितीय फलन प्रश्नावली 3.3 का हल हिंदी में
• त्रिकोणमितीय फलन प्रश्नावली 3.4 का हल हिंदी में
• त्रिकोणमितीय फलन विविध प्रश्नावली का हल हिंदी में
• Trigonometry Formulas
• Trigonometry Functions Class 11 Notes
• NCERT Exemplar Class 11 Maths Chapter 3 Trigonometric Functions
• Trig Cheat Sheet
• JEE Main Trigonometry Previous Year Questions

Free download NCERT Solutions for Class 11 Maths Chapter 3 Trigonometric Functions Ex 3.1, Ex 3.2, Ex 3.3, Ex 3.4, and Miscellaneous Exercise PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.1

Ex 3.1 Class 11 Maths Question 1: Find the radian measures corresponding to the following degree measures: (i) 25° (ii) – 47° 30′ (iii) 240° (iv) 520° Ans:

(i) \(\frac{11}{16}\) We know that: π radian = 180° ∴ \(\frac{11}{16}\) radain = \(\frac{180}{\pi} \times \frac{11}{16}\) × degree

= \(\frac{45 \times 11}{\pi \times 4}\) degree

= \(\frac{45 \times 11 \times 7}{22 \times 4}\) degree

= \(\frac{315}{8}\) degree

= 39 \(\frac{3}{8}\) degree

= 39° + \(\frac{3 \times 60}{8}\) minutes [1° = 60′]

= 39° + 22′ + \(\frac{1}{2}\) minutes

= 39°22’30” [1′ = 60°].

More Resources for CBSE Class 11

NCERT Solutions

• NCERT Solutions Class 11 Maths
• NCERT Solutions Class 11 Physics
• NCERT Solutions Class 11 Chemistry
• NCERT Solutions Class 11 Biology
• NCERT Solutions Class 11 Hindi
• NCERT Solutions Class 11 English
• NCERT Solutions Class 11 Business Studies
• NCERT Solutions Class 11 Accountancy
• NCERT Solutions Class 11 Psychology
• NCERT Solutions Class 11 Entrepreneurship
• NCERT Solutions Class 11 Indian Economic Development
• NCERT Solutions Class 11 Computer Science

Ex 3.1 Class 11 Maths Question 3: A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second? Ans: Number of revolutions made by the wheel in 1 minute = 360 ∴ Number of revolutions made by the wheel in 1 second = \(\frac{360}{6}\) = 6 In one complete revolution, the wheel turns an angle of 2π radian. Hence, in 6 complete revolutions, it will turn an angle of 6 × 2π radian, i.e., 12π radian Thus, in one second, the wheel turns an angle of 12π radian. Ex 3.1 Class 11 Maths Question 4: Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm y an arc of length 22 cm (Use π = \(\frac{22}{7}\)). Ans:

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = \(\frac{l}{r}\) Therefore, for r = 100 cm, l = 22 cm, we have

Thus, the required angle is 12°36′.

Ex 3.1 Class 11 Maths Question 5: In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord. Ans:

Given, diameter = 40 cm ∴ radius (r) = \(\frac{40}{2}\) = 20 cm and length of chord, AB = 20 cm Thus, ∆OAB is an equilateral triangle. We know that, θ = \(\frac{\text { Arc } A B}{\text { radius }}\) ⇒ Arc AB = θ × r = \(\frac{\pi}{3}\) × 20 . = \(\frac{20}{3}\) π cm.

Ex 3.1 Class 11 Maths Question 6: If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii. Ans:

Let the radii of the two circles be r 1  and r 2 . Let an arc of length l subtend an angle of 60° at the centre of the circle of radius r 1 , while let an arc of length l subtend an angle of 75° at the centre of the circle of radius r 2 . Now, 6o° = \(\frac{\pi}{3}\) radian and 75° = \(\frac{5 \pi}{12}\) radian We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = \(\frac{l}{r}\) or l = rθ ∴ l = \(\frac{r_{1} \pi}{3}\) and

l = \(\frac{r_{2} 5 \pi}{12}\)

⇒ \(\frac{r_{1} \pi}{3}=\frac{r_{2} 5 \pi}{12}\)

⇒ r = \(\frac{r_{2} 5}{4}\)

\(\frac{r_{1}}{r_{2}}=\frac{5}{4}\) Thus, the ratio of the radii is 5 : 4.

Ex 3.1 Class 11 Maths Question 7: Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length (i) 10 cm (ii) 15 cm (iii) 21 cm. Ans:

We know that in a circle of radius r unit, if an arc of length l unit subtends an angle θ radian at the centre, then θ = \(\frac{l}{r}\). It is given that r = 75 cm

(i) Here, l = 10 cm θ = \(\frac{10}{75}\) radian = \(\frac{2}{15}\) radian

(ii) Here, l = 15 cm θ = \(\frac{15}{75}\) radian θ = \(\frac{1}{5}\) radian

(iii) Here, l = 21 cm θ = \(\frac{21}{75}\) radian = \(\frac{7}{75}\) radian.

NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.2

sin x = \(\frac{3}{5}\)

cosec x = \(\frac{1}{\sin x}=\frac{1}{\left(\frac{3}{5}\right)}=\frac{5}{3}\) sin 2  x + cos 2  x = 1 ⇒ cos 2  x = 1 – sin 2  x ⇒ cos 2  x = 1 – (\(\frac{3}{5}\)) 2

⇒ cos 2  x = 1 – \(\frac{9}{25}\)

⇒ cos 2  x = \(\frac{16}{25}\)

⇒ cos x = ± \(\frac{4}{5}\) Since x lies in the 2nd quadrant, the value of cos x will be negative

⇒ \(\frac{4}{3}=\frac{\sin x}{\frac{-3}{5}}\) ⇒ sin x = \(\left(\frac{4}{3}\right) \times\left(\frac{-3}{5}\right)=-\frac{4}{5}\) ⇒ cosec x = \(\frac{1}{\sin x}=-\frac{5}{4}\).

tan x = – \(\frac{5}{12}\)

cot x = \(\frac{1}{\tan x}=\frac{1}{\left(-\frac{5}{12}\right)}=-\frac{12}{5}\)

Ex 3.2 Class 11 Maths Question 6: Find the value of the trigonometric function sin 765°. Ans: It is known that the values of sin x repeat after an interval of 2π or 360°. ∴ sin 765° = sin (2 × 360° + 45°) = sin 45° = 1 Ex 3.2 Class 11 Maths Question 7: Find the value of the trigonometric function cosec (- 1410°) Ans: It is known that the values of cosec x repeat after an interval of 2π or 360°. ∴ cosec (- 1410°) = cosec (- 1410° + 4 x 360°) = cosec (- 1410° + 1440°) = cosec 30° = 2. Ex 3.2 Class 11 Maths Question 8: Find the value of the trigonometric function tan \(\frac{19 \pi}{3}\). Ans:

It is known that the values of tan x repeat after an interval of π or 180°. ∴ \(\tan \frac{19 \pi}{3}=\tan 6 \frac{1}{3} \pi\)

= \(\tan \left(6 \pi+\frac{\pi}{3}\right)=\tan \frac{\pi}{3}\)

= tan 60° = √3.

Ex 3.2 Class 11 Maths Question 9: Find the value of the trigonometric function sin \(\left(-\frac{11 \pi}{3}\right)\). Ans:

It is known that the values of cot x repeat after an interval of π or 180°.

∴ \(\sin \left(\frac{11 \pi}{3}\right)=\sin \left(-\frac{11 \pi}{3}+2 \times 2 \pi\right)\)

= \(\sin \left(\frac{\pi}{3}\right)=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\)

Ex 3.2 Class 11 Maths Question 10: Find the value of the trigonometric function cot \(\left(-\frac{15 \pi}{4}\right)\). Ans:

It is known that the values of cot x repeat after an interval of ir or 1800. ∴ \(\cot \left(-\frac{15 \pi}{4}\right)=\cot \left(-\frac{15 \pi}{4}+4 \pi\right)=\cot \frac{\pi}{4}\) = 1.

NCERT Solutions for Class 11 Maths Chapter 3 Exercise 3.3

Ex 3.3 Class 11 Maths Question 1:

Prove that: sin 2  \(\frac{\pi}{6}\) + cos 2  \(\frac{\pi}{3}\) – tan 2  \(\frac{\pi}{4}\) = – \(\frac{1}{2}\) Ans:

L.H.S.= sin 2  \(\frac{\pi}{6}\) + cos 2  \(\frac{\pi}{3}\) – tan 2  \(\frac{\pi}{4}\)

= \(\left(\frac{1}{2}\right)^{2}+\left(\frac{1}{2}\right)^{2}\) – (1) 2

= \(\frac{1}{4}+\frac{1}{4}-1=-\frac{1}{2}\)

= R.H.S. Hence proved.

L.H.S = \(2 \sin ^{2} \frac{3 \pi}{4}+2 \cos ^{2} \frac{\pi}{4}+2 \sec ^{2} \frac{\pi}{3}\)

= \(2\left\{\sin \left(\pi-\frac{\pi}{4}\right)\right\}^{2}+2\left(\frac{1}{\sqrt{2}}\right)^{2}+2(2)^{2}\)

= \(2\left\{\sin \frac{\pi}{4}\right\}^{2}+2 \times \frac{1}{2}+8\)

= 2 \(\left(\frac{1}{\sqrt{2}}\right)^{2}\) + 1 + 8

= 1 + 1 + 8 = 10 = R.H.S. Hence proved.

Ex 3.3 Class 11 Maths Question 5: Find the value of: (i) sin 75°, (ii) tan 15° Ans:

(i) sin 75° sin (45° + 30°) = sin 45° cos 30° + cos 45° sin 30° [∵ sin (x + y) = sin x cos y + cos x sin y] = \(\left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{2}\right)+\left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}\right)\)

= \(\frac{\sqrt{3}}{2 \sqrt{2}}+\frac{1}{2 \sqrt{2}}=\frac{\sqrt{3}+1}{2 \sqrt{2}}\)

(ii) tan 15° = tan (45° – 30°)

L.H.S = \(\frac{\cos (\pi+x) \cos (-x)}{\sin (\pi-x) \cos \left(\frac{\pi}{2}+x\right)}\)

= \(\frac{[-\cos x][\cos x]}{(\sin x)(-\sin x)}=\frac{-\cos ^{2} x}{-\sin ^{2} x}\)

= R.H.S Hence proved.

It is known that cos A – cos B = \(-2 \sin \left(\frac{A+B}{2}\right) \cdot \sin \left(\frac{A-B}{2}\right)\)

∴ L.H.S.= \(=\cos \left(\frac{3 \pi}{4}+x\right)-\cos \left(\frac{3 \pi}{4}-x\right)\)

= \(– 2 \sin \left\{\frac{\left(\frac{3 \pi}{4}+x\right)+\left(\frac{3 \pi}{4}-x\right)}{2}\right\} \cdot \sin \left\{\frac{\left(\frac{3 \pi}{4}+x\right)-\left(\frac{3 \pi}{4}-x\right)}{2}\right\}\)

= – 2 sin (\(\frac{3 \pi}{4}\)) sin x

= – 2 sin (- \(\frac{\pi}{4}\)) sin x

= – √2 sin x = R.H.S. Hence proved.

Ex 3.3 Class 11 Maths Question 12: Prove that: sin 2  6x – sin 2  4x = sin 2x sin 10 x Ans:

It is known that sin A + sin B = 2 \(\sin \left(\frac{A-B}{2}\right) \cos \left(\frac{A-B}{2}\right)\)

sin A – sin B = 2 \(\cos \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)\) L.H.S.= sin 2  6x – sin 2  4x = (sin 6x + sin 4x) (sin 6x – sin 4x) = (2 sin 5x cos x) (2 cos 5x sin x) = (2 sin 5x cos 5x) (2 sin x cos x) = sin 10x sin 2x = R.H.S. Hence proved.

Ex 3.3 Class 11 Maths Question 13: Prove that: cos 2  2x cos 2  6x = sin 4x sin 8x Ans:

It is known that cos A + cos B = 2 \(\cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\)

cos A – cos = 2 \(\sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)\)

∴ L.H.S = cos 2  2x – cos 2  6x = (cos 2x + cos 6x) (cos 2x – 6x) = \(\left[2 \cos \left(\frac{2 x+6 x}{2}\right) \cos \left(\frac{2 x-6 x}{2}\right)\right]\left[-2 \sin \left(\frac{2 x+6 x}{2}\right) \sin \frac{(2 x-6 x)}{2}\right]\) ∴ L.H.S.= cos 2  2x – cos 2  6x = (cos 2x + cos 6x) (cos 2x – 6x) = [2 cos 4x cos (-2x)] [- 2 sin 4x sin (- 2x)] = [2 cos 4x cos 2x] [- 2 sin 4x (- sin 2x)] = (2 sin 4x cos 4x) (2 sin 2x cos 2x) = sin 8x sin 4x = R.H.S. Hence proved.

It is known that sin A + sin = 2 \(\sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\)

cos A + cos = 2 \(\cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\)

∴ L.H.S = \(\frac{\sin 5 x+\sin 3 x}{\cos 5 x+\cos 3 x}\)

= \(\frac{2 \sin \left(\frac{5 x+3 x}{2}\right) \cos \left(\frac{5 x-3 x}{2}\right)}{2 \cos \left(\frac{5 x+3 x}{2}\right) \cos \left(\frac{5 x-3 x}{2}\right)}\)

= \(\frac{2 \sin 4 x \cos x}{2 \cos 4 x \cos x}=\frac{\sin 4 x}{\cos 4 x}\)

= tan 4x = R.H.S. Hence proved.

It is known that sin A – sin B = 2 \(\cos \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)\)

cos 2  A – sin 2  A = cos 2A

∴ L.H.S. = \(=\frac{\sin x-\sin 3 x}{\sin ^{2} x-\cos ^{2} x}\)

= \(\frac{2 \cos \left(\frac{x+3 x}{2}\right) \sin \left(\frac{x-3 x}{2}\right)}{-\cos 2 x}\)

= \(\frac{2 \cos 2 x \sin (-x)}{-\cos 2 x}\)

= – 2 × (- sin x) = 2 sin x

Hence proved.

Class 11 Maths NCERT Solutions Chapter 3 Exercise 3.4

cos 4x = cos 2x cos 4x – cos 2x = 0 – 2 sin \(\left(\frac{4 x+2 x}{2}\right)\) sin \(\left(\frac{4 x-2 x}{2}\right)\) = 0

[∵ cos A – cos B = 2 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)\(\)]

sin 3x sin x = 0 sin 3x = 0or sin x = 0 3x = nπ or x = nπ, where n ∈ Z x = \(\frac{n \pi}{3}\) or x = nπ, where n ∈ Z.

Ex 3.4 Class 11 Maths Question 6: Find the general solution of the equation cos 3x + cosx – cos 2x = 0 Ans:

cos 3x + cos x – cos 2x = 0 2 cos \(\left(\frac{3 x+x}{2}\right)\) cos \(\left(\frac{3 x-x}{2}\right)\) – cos 2x = 0

[∵ cos A + cos B = 2 \(\cos \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\)]

2 cos 2x cos x – cos 2x = 0 cos 2x (2 cos x – 1) = 0 cos 2x = 0 or 2 cos x – 1 = 0 cos 2x = 0 or cos x = \(\frac{1{2}\) ∴ 2x = (2n + 1) \(\frac{\pi}{2}\) or cos x = cos \(\frac{\pi}{3}\), where n ∈ Z x = (2n + 1) \(\frac{\pi}{4}\) or x = 2nπ ± \(\frac{\pi}{3}\) where n ∈ Z.

Ex 3.4 Class 11 Maths Question 7: Find the general solution of the equation sin 2x + cos x = 0 Ans:

sin 2x + cos x = 0 ⇒ 2sin x cos x + cos x = 0 ⇒ cos x (2 sin x + 1) = 0 ⇒ cos x = 0 or 2 sin x + 1 = 0 Now, cos x = 0 ⇒ x = (2n + 1) \(\frac{\pi}{2}\) , where n ∈ Z. or 2 sin x + 1 = 0 ⇒ sin x = – \(\frac{1}{2}\)

= – sin \(\frac{\pi}{6}\)

= sin (π + \(\frac{\pi}{6}\))

= sin \(\frac{7 \pi}{6}\)

x = nπ + (- 1) n  \(\frac{7 \pi}{6}\) where n ∈ Z Therefore, the general solution is (2n + 1) \(\frac{\pi}{2}\) or nπ + (- 1) n  \(\frac{7 \pi}{6}\) where n ∈ Z.

Ex 3.4 Class 11 Maths Question 8: Find the general solution of the equation sec 2  2x = 1 – tan 2x. Ans:

sec 2  2x = 1 – tan 2x 1 + tan 2  2x = 1 – tan 2x tan 2  x + tan 2x = 0 => tan 2x (tan 2x + 1) = 0 => tan 2x = 0 or tan 2x + 1 = 0 Now, tan 2x = 0 => tan 2x = tan 0 2x = nπ + 0, where n ∈ Z x = \(\frac{n \pi}{2}\), where n ∈ Z or tan 2x + 1 = 0 = tan 2x = – 1 = – tan \(\frac{\pi}{4}\)

= tan (π – \(\frac{\pi}{4}\))

= tan \(\frac{3 \pi}{4}\)

2x = nπ + \(\frac{3 \pi}{4}\) where n ∈ Z

x = \(\frac{n \pi}{2}+\frac{3 \pi}{8}\), where n ∈ Z

Therefore, the general solution is \(\frac{n \pi}{2}\) or \(\frac{n \pi}{2}+\frac{3 \pi}{8}\) where n ∈ Z.

Ex 3.4 Class 11 Maths Question 9: Find the general solution of the equation sin x + sin 3x + sin 5x = 0 Ans:

sin x + sin 3x + sin 5x = 0 ⇒ (sin x + sin 5x) + sin 3x = 0

\(\left[2 \sin \left(\frac{x+5 x}{2}\right) \cos \left(\frac{x-5 x}{2}\right)\right]\) + sin 3x = 0

[∵ sin A + sin B = 2 sin \(\sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)\)]

2 sin 3x cos (2x) + sin 3x = 0 2 sin 3x cos 2x + sin 3x = 0 sin 3x (2 cos 2x +1) = 0 sin 3x = 0 or 2 cos 2x + 1 = 0 Now sin 3x = 0 ⇒ 3x = nπ, where n ∈ Z i.e., x = \(\frac{n \pi}{3}\) where n ∈ Z or 2 cos 2x + 1 = 0 cos 2x = \(-\frac{1}{2}\)

= – cos \(\frac{\pi}{3}\)

= cos (π – \(\frac{\pi}{3}\))

cos 2x = cos \(\frac{2 \pi}{3}\)

⇒ 2x = 2nπ ± \(\frac{2\pi}{3}\), where n ∈ Z

⇒ x = nπ ± \(\frac{\pi}{3}\), where n ∈ Z

Therefore, the general solution is \(\frac{n \pi}{3}\) or nπ ± \(\frac{\pi}{3}\), where n ∈ Z.

NCERT Solutions for Class 11 Maths Chapter 3 Miscellaneous Exercise

L.H.S. = (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = sin 3x sin x + sin 2  x + cos 3x cos x – cos 2  x = cos 3x cos x + sin 3x sin x – (cos 2  x – sin 2  x) = cos (3x – x) – cos 2x [∵ cos(A – B) = cos A cos B + sin A sin B] = cos 2x – cos 2x = 0 =R.H.S. Hence proved.

Miscellaneous Exercise Class 11 Maths Question 3:

Prove that: (cos x + cos y) 2  + (sin x – sin y) 2  = 4 cos 2  \(\left(\frac{x+y}{2}\right)\)

L.H.S.= (cos x + cos y) 2  + (sin x – sin y) 2 = cos 2  x + cos 2  y + 2 cos x cos y + sin 2  x + sin 2  y – 2 sin x sin y = (cos 2  x + sin 2  x) + (cos 2  y + sin 2  y) + 2 (cos x cos y – sin x sin y) = 1 + 1 + 2 cos (x + y) [∵ cos (A + B) = (cos A cos B – sin A sin B)] = 2 + 2 cos (x + y) = 2 [1 + cos (x + y)] = 2[1 + \(2 \cos ^{2}\left(\frac{x+y}{2}\right)\) – 1] [∵ cos 2A = 2 cos 2  A – 1] = 4 c0s 2  \(\left(\frac{x+y}{2}\right)\) = R.H.S. Hence proved.

Miscellaneous Exercise Class 11 Maths Question 4: Prove that: (cos x – cos y) 2  + (sin x – sin y) 2  = 4 sin 2  \(\frac{x-y}{2}\) Ans:

L.H.S.= (cos x – cos y) 2  + (sin x – sin y) 2 = cos 2  x + cos 2  y – 2 cos x cos y + sin 2  x + sin 2  y – 2 sin x sin y = (cos 2  x + sin 2  x) + (cos 2  y + sin 2  y) – 2 [cos x cos y + sin x sin y] = 1 + 1 – 2 [cos (x – y)] = 2 [1 – {1 – 2 sin 2  \(\left(\frac{x-y}{2}\right)\)}] [∵ cos 2A = 1 – 2 sin 2  A] = 4 sin 2  \(\left(\frac{x-y}{2}\right)\) = R.H.S. Hence proved.

Miscellaneous Exercise Class 11 Maths Question 5: Prove that: sin x + sin 3x + sin 5x + sin 7x = 4 cos x cos 2x sin 4x Ans:

It is known that sin A + sin B = 2 \(\sin \left(\frac{A+B}{2}\right) \cdot \cos \left(\frac{A-B}{2}\right)\) ∴ L.H.S. = (sin x + sin 3x) + (sin 5x + sin 7x) = (sin x + sin 5x) + (sin 3x + sin 7x) = \(2 \sin \left(\frac{x+5 x}{2}\right)\) . \(\cos \left(\frac{x-5 x}{2}\right)+2 \sin \left(\frac{3 x+7 x}{2}\right) \cos \left(\frac{3 x-7 x}{2}\right)\) = 2 sin 3x cos (- 2x) + 2 sin 5x cos (- 2x) = 2 sin 3x cos 2x + 2 sin 5x cos 2x = 2 cos 2x [sin 3x + sin 5x] = 2 cos 2x [latex]2 \sin \left(\frac{3 x+5 x}{2}\right) \cdot \cos \left(\frac{3 x-5 x}{2}\right)[/latex] = 2 cos 2x [2 sin 4x . cos (- x)] = 4 cos 2x sin 4x cos x = R.H.S. Hence proved.

Miscellaneous Exercise Class 11 Maths Question 6: Prove that: \(\frac{(\sin 7 x+\sin 5 x)+(\sin 9 x+\sin 3 x)}{(\cos 7 x+\cos 5 x)+(\cos 9 x+\cos 3 x)}\) = tan 6x Ans: It is known that

प्रश्न 3. एक-पहिया एक मिनट में 360° परिक्रमण करता है तो एक सेकंड में कितने रेडियन माप का कोण बनाएगा? हल: परिक्रमण में पहिया द्वारा बना कोण = 27 रेडियन 360 परिक्रमण में पहिया द्वारा बना कोण = 360 x 2π रेडियन 1 मिनट अर्थात् 60 सेकण्ड में 360 x 2π रेडियन का कोण बनता है। 1 सेकण्ट में चहिया द्वारा बना कोण = \(\frac { 360\times 2\pi }{ 60 }\) = 12π रेडियन।

Exercise 3.1

Q.1: Calculate the radian measurement of the given degree measurement:

(ii). 240 ∘

(iii). − 47 ∘ 30 ‘

(iv). 520 ∘

Q.2: Calculate the degree measurement of the given degree measurement: [Use π = \(\\ \frac { 22 }{ 7 } \)]

(i) \(\\ \frac { 11 }{ 16 } \)

(iii) \(\frac { 5\pi }{ 3 } \)

(iv) \(\frac { 7\pi }{ 6 } \)

Q.3: In a minute, wheel makes 360 revolutions. Through how many radians does it turn in 1 second?

Q.4: Calculate the degree measurement of the angle subtended at the centre of a circle of radius 100 m by an arc of length 22 m.

Q.5: In a circle of diameter 40 m, the length of the chord 20 m. Find the length of minor arc of chord.

Q.6: In two circles, arcs which has same length subtended at an angle of 60 ∘ and 75 ∘ at the center. Calculate the ratio of their radii.

Q.7: Calculate the angle in radian through which a pendulum swings if the length is 75 cm and the tip describes an arc of length

(iii) 21 cm

Exercise 3.2

Q.1: Calculate the values of five trigonometric func. if cos y = \(– \frac { 1 }{ 2 } \) and y lies in 3 rd quadrant.

(iii) cosec y

Q.2: Calculate the other five trigonometric function if we are given the values for sin y = \(\\ \frac { 3 }{ 5 } \), where y lies in second quadrant.

Q.3: Find the values of other five trigonometric functions if c o t y =\(\\ \frac { 3 }{ 4 } \) , where y lies in the third quadrant.

Q.4: Find the values of other five trigonometric if s e c y =\(\\ \frac { 13 }{ 5 } \) , where y lies in the fourth quadrant.

Q.5: Find the values of other five trigonometric function if tan y = \(– \frac { 5 }{ 12 } \) and y lies in second quadrant.

Q.6: Calculate the value of trigonometric function sin 765°.

Q.7: Calculate the value of trigonometric function cosec [-1410°]

Q.8: Calculate the value of the trigonometric function tan \(\frac { 19\pi }{ 3 } \) .

Q.9: Calculate the value of the trigonometric function sin \(-\frac { 11\pi }{ 3 } \) .

Q.10: Calculate the value of the trigonometric function cot \(-\frac { 15\pi }{ 4 } \)

Exercise 3.3

Q.1: Prove:

sin²\(\frac { \pi }{ 6 } \) + cos² \(\frac { \pi }{ 3 } \) – tan² \(\frac { \pi }{ 4 } \) = \(– \frac { 1 }{ 2 } \)

Q.2: Prove:

2 sin² \(\frac { \pi }{ 6 } \) + c o s e c ² \(\frac { 7\pi }{ 6 } \) 6 cos ² \(\frac { \pi }{ 3 } \) =\(\\ \frac { 3 }{ 2 } \)

Q.3: Prove:

cot ² \(\frac { \pi }{ 6 } \) + c o s e c \(\frac { 5\pi }{ 6 } \) + 3 tan ² latex s=2]\frac { \pi }{ 6 } [/latex] = 6

Q.4: Prove:

2 sin ² \(\frac { 3\pi }{ 4 } \) + 2 cos ² \(\frac { \pi }{ 4 } \) + 2 sec ² \(\frac { \pi }{ 3 } \) = 10

Q.5: Calculate the value of:

(i). sin 75 ∘

(ii). tan 15 ∘

cos ( \(\frac { \pi }{ 4 } \) – x ) cos ( \(\frac { \pi }{ 4 } \) – y ) – sin ( \(\frac { \pi }{ 4 } \) – x ) sin ( \(\frac { \pi }{ 4 } \) – y ) = sin ( x + y )

Q.7: Prove:

\(\frac { tan(\frac { \pi }{ 4 } +x) }{ tan(\frac { \pi }{ 4 } -x) } ={ \left( \frac { 1+tanx }{ 1-tanx } \right) }^{ 2 }\)

Q.8: Prove:

\(\frac { cos(\pi +x)cos(-x) }{ sin(\pi -x)cos\left( \frac { \pi }{ 2 } +x \right) } ={ cot }^{ 2 }x\)

Q.9: Prove:

\(cos(\frac { 3\pi }{ 2 } +x)cos(2\pi +x)[cot(\frac { 3\pi }{ 2 } -x)+cot(2\pi +x)]=1\)

Q.10: Prove:

sin ( n + 1 ) x sin ( n + 2 ) x + cos ( n + 1 ) x cos ( n + 2 ) x = cos x

Q.11 Prove:

\(cos(\frac { 3\pi }{ 4 } +x)-cos(\frac { 3\pi }{ 4 } -x)\)= − √2 sin x

Q.12: Prove:

sin² 6 x – sin ² 4 x = sin2 x sin 10 x

Q.13: Prove:

cos ² 2 x – cos ² 6 x = sin 4 x sin 8 x

Q.14:Prove:

sin 2 x + 2 sin 4 x + sin 6 x = 4 cos ² x sin 4 x

Q.15: Prove:

cot 4 x ( sin 5 x + sin 3 x ) = cot x ( sin 5 x – sin 3 x )

Q.16: Prove:

\(\frac { cos9x-cos5x }{ sin17x-sin3x } =-\frac { sin2x }{ cos10x } \)

Q.17: Prove:

\(\frac { sin5x+sin3x }{ cos5x+cos3x } =tan4x\)

Q.18: Prove:

\(\frac { sinx-siny }{ cosx+cosy } =tan\frac { x-y }{ 2 } \)

Q.19: Prove:

\(\frac { sinx+sin3x }{ cosx+cos3x } =tan2x\)

Q.20: Prove:

\(\frac { sinx-sin3x }{ { sin }^{ 2 }x-{ cos }^{ 2 }x } =2sinx\)

Q.21: Prove:

\(\frac { cos4x+cos3x+cos2x }{ sin4x+sin3x+sin2x } =cot3x\)

Q.22: Prove:

cot x cot 2 x – cot 2 x cot 3 x – cot 3 x cot x = 1

Q.23: Prove:

\(tan4x=\frac { 4tanx(1-{ tan }^{ 2 }x) }{ 1-6{ tan }^{ 2 }x+{ tan }^{ 4 }x } \)

Q.24: Prove:

cos 4 x = 1 – 8 sin² x cos² x

Q.25: Prove:

cos 6 x = 32 cos 6 x – 48 cos 4 x + 18 cos 2 x − 1

Exercise 3.4

Q.1: Find general solutions and the principle solutions of the given equation: tan x = √3

Q.2: Find general solutions and the principle solutions of the given equation: sec x = 2

Q.3: Find general solutions and the principle solutions of the given equation: cot = − √3

Q.4: Find general solutions and the principle solutions of the given equation: cosec x = -2

Q.5: Find the general solution of the given equation: cos 4x = cos 2x

Q.6: Find the general solution of the given equation: cos 3x + cos x – cos 2x = 0

Q.7: Find the general solution of the given equation: sin 2x + cos x = 0

Q.8: Find the general solution of the given equation: sec² 2 x = 1 – tan 2 x

Q.9: Find the general solution of the given equation: sin x + sin 3x + sin 5x = 0

Miscellaneous Exercise

Q.1: Prove that:

\(2cos\frac { \pi }{ 13 } cos\frac { 9\pi }{ 13 } +cos\frac { 3\pi }{ 13 } +cos\frac { 5\pi }{ 13 } =0\)

Q.2: Prove that:

( sin 3 x + sin x ) sin x + ( cos 3 x – cos x ) cos x = 0

Q-3: Prove that:

( cos x + cos y )² + ( sin x – sin y ) ² = 4 cos ²\(\\ \frac { x+y }{ 2 } \)

Q-4: Prove that:

( cos x – cos y ) ² + ( sin x – sin y ) ² = 4 sin ² \(\\ \frac { x-y }{ 2 } \)

Q-5: Prove that:

sin x + sin 3 x + sin 5 x + sin 7 x = 4 cos x cos 2 x cos 4 x

Q-6: Prove that:

\(\frac { (sin7x+sin5x)+(sin9x+sin3x) }{ (cos7x+cos5x)+(cos9x+cos3x) } =tan6x\)

Q-7: Show that: sin 3 y + sin 2 y – sin y = 4 sin y cos\(\\ \frac { y }{ 2 } \) cos\(\\ \frac { 3y }{ 2 } \)

Q-8: The value of tan y =\(– \frac { 4 }{ 2 } \) where y in in 2 nd quadrant then find out the values of sin\(\\ \frac { y }{ 2 } \) , cos\(\\ \frac { y }{ 2 } \) a n d tan\(\\ \frac { y }{ 2 } \) .

Q-9: The value of cos y = \(– \frac { 1 }{ 3 } \) where y in in 3 rd quadrant then find out the values of sin \(\\ \frac { y }{ 2 } \) , cos \(\\ \frac { y }{ 2 } \) a n d tan \(\\ \frac { y }{ 2 } \) .

Q-10: The value of sin y = \(\\ \frac { 1 }{ 4 } \) where y in in 2 nd quadrant then find out the values of sin \(\\ \frac { y }{ 2 } \) , cos \(\\ \frac { y }{ 2 } \) a n d tan \(\\ \frac { y }{ 2 } \) .

NCERT Solutions for Class 11 Maths All Chapters

• Chapter 1 Sets
• Chapter 2 Relations and Functions
• Chapter 3 Trigonometric Functions
• Chapter 4 Principle of Mathematical Induction
• Chapter 5 Complex Numbers and Quadratic Equations
• Chapter 6 Linear Inequalities
• Chapter 7 Permutation and Combinations
• Chapter 8 Binomial Theorem
• Chapter 9 Sequences and Series
• Chapter 10 Straight Lines
• Chapter 11 Conic Sections
• Chapter 12 Introduction to Three Dimensional Geometry
• Chapter 13 Limits and Derivatives
• Chapter 14 Mathematical Reasoning
• Chapter 15 Statistics
• Chapter 16 Probability

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Some advantages of Free Assignments for Class 11 Mathematics

• Solving Assignments for Mathematics Class 11 helps to further enhance understanding of the topics given in your text book which will help you to get better marks
• By solving one assignments given in your class by Mathematics teacher for class 11 will help you to keep in touch with the topic thus reducing dependence on last minute studies
• You will be able to understand the type of questions which are expected in your Mathematics class test
• You will be able to revise all topics given in the ebook for Class 11 Mathematics as all questions have been provided in the question banks
• NCERT Class 11 Mathematics Workbooks will surely help you to make your concepts stronger and better than anyone else in your class.
• Parents will be able to take print out of the assignments and give to their child easily.

All free Printable practice assignments are in PDF single lick download format and have been prepared by Class 11 Mathematics teachers after full study of all topics which have been given in each chapter so that the students are able to take complete benefit from the worksheets. The Chapter wise question bank and revision assignments can be accessed free and anywhere. Go ahead and click on the links above to download free CBSE Class 11 Mathematics Assignments PDF.

You can download free assignments for class 11 Mathematics from https://www.assignmentsbag.com

You can get free PDF downloadable assignments for Grade 11 Mathematics from our website which has been developed by teachers after doing extensive research in each topic.

On our website we have provided assignments for all subjects in Grade 11, all topic wise test sheets have been provided in a logical manner so that you can scroll through the topics and download the worksheet that you want.

You can easily get question banks, topic wise notes and questions and other useful study material from https://www.assignmentsbag.com without any charge

Yes all test papers for Mathematics Class 11 are available for free, no charge has been put so that the students can benefit from it. And offcourse all is available for download in PDF format and with a single click you can download all assignments.

https://www.assignmentsbag.com is the best portal to download all assignments for all classes without any charges.

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• Math Article

Class 11 Maths Index

Class 11 maths index page given here covers all the chapters and their sub-topics that are included in the class 11 maths book of NCERT. These topics covered in this index page contains all the syllabus concepts that are prescribed by the CBSE. These CBSE maths syllabus topics are covered in an easy to understand the way to help students have a deeper understanding of the topics.

It should be noted that class 11 is an important phase as the syllabus topics are not only important for the class 11 exam but are also crucial for competitive exams like JEE. These topic-wise index page can be beneficial for students to go through all the topics easily quickly.

The main units in CBSE class 11 maths syllabus are:

• Sets and Functions
• Coordinate Geometry
• Statistics and Probability
• Mathematical Reasoning

Unit – I: Sets and Functions

Chapter 1: sets.

• Sets and Their Representations
• Finite and Infinite Sets
• Subsets of a set of real numbers especially intervals (with notations)
• Universal Set
• Venn Diagrams
• Union and Intersection of Sets
• Difference of Sets
• Complement of a Set
• Properties of Complement

Chapter 2: Relations & Functions

• Ordered pairs and Cartesian product of sets
• Number of elements in the cartesian product of two finite sets
• Cartesian product of the sets of real (up to R × R)
• Definition of −
• Pictorial diagrams
• Domain, Co-domain and Range of a relation
• Function as a special kind of relation from one set to another
• Pictorial representation of a function, domain, co-domain and range of a function
• Exponential
• Logarithmic
• Greatest integer functions (with their graphs)
• Sum, difference, product and quotients of functions

Chapter 3: Trigonometric Functions

• Introduction to Trigonometric Functions
• Positive and negative angles
• Measuring angles in radians and in degrees and conversion of one into other
• Definition of trigonometric functions with the help of unit circle
• Truth of the sin 2 x + cos 2 x = 1, for all x
• Signs of trigonometric functions
• Domain and range of trigonometric functions
• Graphs of Trigonometric Functions
• Expressing sin (x±y) and cos (x±y) in terms of sinx, siny, cosx & cosy and their simple application
• Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x
• General solution of trigonometric equations of the type sin y = sin a, cos y = cos a and tan y = tan a

Unit – II: Algebra

Chapter 4: principle of mathematical induction.

• Introduction to Principle of Mathematical Induction
• Process of the proof by induction −
• Motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers
• The principle of mathematical induction and simple applications

Chapter 5: Complex Numbers and Quadratic Equations

• Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic equations
• Algebraic properties of complex numbers
• Argand plane and polar representation of complex numbers
• Statement of Fundamental Theorem of Algebra
• Solution of quadratic equations in the complex number system
• Square root of a complex number

Chapter 6: Linear Inequalities

• Introduction to Linear inequalities
• Algebraic solutions of linear inequalities in one variable and their representation on the number line
• Graphical solution of linear inequalities in two variables
• Graphical solution of system of linear inequalities in two variables

Chapter 7: Permutations and Combinations

• Introduction to Permutations and Combinations
• Fundamental principle of counting
• Factorial n
• (n!) Permutations and combinations
• Derivation of formulae and their connections
• Simple applications

Chapter 8: Binomial Theorem

• Statement and proof of the binomial theorem for positive integral indices
• Pascal’s triangle
• General and middle term in binomial expansion

Chapter 9: Sequence and Series

• Sequence and Series
• Arithmetic Progression (A.P.)
• Arithmetic Mean (A.M.)
• Geometric Progression (G.P.)
• Arithmetic and Geometric series infinite G.P. and its sum
• Geometric mean (G.M.)
• Relation between A.M. and G.M.

Unit – III: Coordinate Geometry

Chapter 10: straight lines.

• Introduction to Straight Lines
• Brief recall of two dimensional geometries from earlier classes
• Shifting of origin
• Slope of a line and angle between two lines
• Various forms of equations of a line −
• Parallel to axis
• Point-slope form
• Slope-intercept form
• Two-point form
• Intercept form
• Normal form
• General equation of a line
• Equation of family of lines passing through the point of intersection of two lines
• Distance of a point from a line

Chapter 11: Conic Sections

• Sections of a cone −
• Hyperbola − a point, a straight line and a pair of intersecting lines as a degenerated case of a conic section.
• Standard equations and simple properties of −
• Standard equation of a circle

Chapter 12: Introduction to Three–dimensional Geometry

• Three–dimensional Geometry
• Coordinate axes and coordinate planes in three dimensions
• Coordinates of a point
• Distance between two points
• Section Formula

Unit-IV: Calculus

Chapter 13: limits and derivatives.

• Derivatives
• Limits of the trigonometric functions
• Algebra of the derivative of the function

Unit-V: Mathematical Reasoning

Chapter 14: mathematical reasoning.

• Introduction to Mathematical Reasoning
• Mathematically acceptable statements
• Connecting words/ phrases
• Validating the statements involving the connecting words difference between contradiction, converse and contrapositive

Unit-VI: Statistics and Probability

Chapter 15: statistics.

• Introduction to Statistics
• Measures of dispersion −
• Mean deviation
• Standard deviation of ungrouped/grouped data
• Analysis of frequency distributions with equal means but different variances.

Chapter 16: Probability

• Probability Introduction
• Random experiments −
• Sample spaces (set representation)
• Types of Events
• Occurrence of events, ‘not’, ‘and’ and ‘or’ events
• Exhaustive events
• Mutually exclusive events
• Axiomatic (set theoretic) probability
• Connections with the theories of earlier classes
• Probability of −
• Probability of ‘not’, ‘and’ and ‘or’ events

Advantages of BYJU’S Class 11 Topic-wise Maths Lessons

Each of the topics from the list mentioned above is explained in an easily understandable manner. Hence, any students of class 11 can quickly grasp and develop a deeper understanding of the fundamentals. Additional information about the topics and sub-topics are also given which will not only help students to prepare for their board exams but will also help them to get confident with their preparation of JEE and other engineering entrance exams.

Keep visiting BYJU’S to get all the maths index pages for all the classes and prepare more effectively. Also, get several class-wise maths sample papers, question papers, formulas and other study materials for additional assistance in mathematics preparation.

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