# NCERT solutions for Class 11 Mathematics Textbook chapter 3 - Trigonometric Functions [Latest edition]

#### Chapters ## Chapter 3: Trigonometric Functions

[Pages 54 - 55]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 3 Trigonometric Functions [Pages 54 - 55]

Q 1.1 | Page 54

Find the radian measures corresponding to the following degree measures:

25°

Q 1.2 | Page 54

Find the radian measures corresponding to the following degree measures:

– 47° 30

Q 1.3 | Page 54

Find the radian measures corresponding to the following degree measures:

240°

Q 1.4 | Page 54

Find the radian measures corresponding to the following degree measures:

520°

Q 2.1 | Page 55

Find the degree measures corresponding to the following radian measures (use  pi = 22/7)

11/16

Q 2.2 | Page 55

Find the degree measures corresponding to the following radian measures (Use pi = 22/7)

-4

Q 2.3 | Page 55

Find the degree measures corresponding to the following radian measures (Use pi = 22/7)

(5pi)/3

Q 2.4 | Page 55

Find the degree measures corresponding to the following radian measures (use pi= 22/7)

(7pi)/6

Q 3 | Page 55

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Q 4 | Page 55

Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm

(Use pi = 22/7)

Q 5 | Page 55

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Q 6 | Page 55

If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

Q 7.1 | Page 55

Find the angle in radian though which a pendulum swings if its length is 75 cm and the tip describes an arc of length

10 cm

Q 7.2 | Page 55

Find the angle in radian though which a pendulum swings if its length is 75 cm and the tip describes an arc of length

15 cm

Q 7.3 | Page 55

Find the angle in radian though which a pendulum swings if its length is 75 cm and the tip describes an arc of length

21 cm

[Page 63]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 3 Trigonometric Functions [Page 63]

Q 1 | Page 63

Find the values of other five trigonometric functions  if cos x = -1/2, x lies in third quadrant.

Q 2 | Page 63

Find the values of other five trigonometric functions if sin x = 3/5 x lies in quadrant

Q 3 | Page 63

Find the values of other five trigonometric functions if cot x = 3/4, x lies in quadrant

Q 4 | Page 63

Find the values of other five trigonometric functions if  sec x = 13/5 , x  lies in fourth quadrant.

Q 5 | Page 63

Find the values of other five trigonometric functions if  tan x = - 5/12, x lies in second quadrant

Q 6 | Page 63

Find the value of the trigonometric function sin 765°

Q 7 | Page 63

Find the value of the trigonometric function cosec (–1410°)

Q 8 | Page 63

Find the value of the trigonometric function tan  (19pi)/3

Q 9 | Page 63

Find the value of the trigonometric function sin (-11pi)/3

Q 10 | Page 63

Find the value of the trigonometric function cot (-(  15pi)/4)

[Pages 73 - 74]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 3 Trigonometric Functions [Pages 73 - 74]

Q 1 | Page 73

Prove that: sin^2  pi/6 + cos^2  pi/3 - tan^2  pi/4 = -1/2

Q 2 | Page 73

Prove that  2 sin^2  pi/6 + cosec^2  (7pi)/6 cos^2  pi/3 = 3/2

Q 3 | Page 73

Prove that  cos^2  pi/6 + cosec (5pi)/6 + 3 tan^2  pi/6 = 6

Q 4 | Page 73

Prove that  2 sin^2  (3pi)/4 + 2 cos^2  pi/4  + 2 sec^2  pi/3  = 10

Q 5.1 | Page 73

Find the value of:  sin 75°

Q 5.2 | Page 73

Find the value of: tan 15°

Q 6 | Page 73

Prove that: cos (pi/4 xx x) cos (pi/4 - y) - sin (pi/4 -  x)sin (pi/4  - y) =  sin (x + y)

Q 7 | Page 73

Prove that (tan(pi/4 + x))/(tan(pi/4 - x)) = ((1+ tan x)/(1- tan x))^2

Q 8 | Page 73

Prove that (cos (pi + x) cos (-x))/(sin(pi - x) cos (pi/2 + x)) =  cot^2 x

Q 9 | Page 73

Prove that cos ((3pi)/ 2 + x ) cos(2pi + x) [cot ((3pi)/2 - x) + cot (2pi + x)]= 1

Q 10 | Page 73

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

Q 11 | Page 73

Prove that cos ((3pi)/4 + x) - cos((3pi)/4 - x) = -sqrt2 sin x

Q 12 | Page 73

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

Q 13 | Page 73

Prove that cos2 2x – cos2 6x = sin 4sin 8x

Q 14 | Page 73

Prove that sin 2x + 2sin 4x + sin 6x = 4cos2 x sin 4x

Q 15 | Page 73

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

Q 16 | Page 73

Prove that  (cos9x - cos5x)/(sin17x - sin 3x) = - (sin2x)/(cos 10x)

Q 17 | Page 73

Prove that (sin 5x + sin 3x)/(cos 5x + cos 3x) = tan 4x

Q 18 | Page 73

Prove that (sin x -  siny)/(cos x + cos y)= tan  (x -y)/2

Q 19 | Page 73

Prove that  (sin x + sin 3x)/(cos x + cos 3x) = tan 2x

Q 20 | Page 73

Prove that (sin x - sin 3x)/(sin^2 x - cos^2 x) =  2sin x

Q 21 | Page 73

Prove that (cos 4x + cos 3x + cos 2x)/(sin 4x + sin 3x + sin 2x) = cot 3x

Q 22 | Page 74

Prove that cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

Q 23 | Page 74

Prove that  tan  4x = (4tan x(1 -  tan^2 x))/(1 -  6tan^2 x + tan^4 z)

Q 24 | Page 73

Prove that cos 4x = 1 – 8sincosx

Q 25 | Page 74

Prove that: cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 – 1

[Pages 3 - 78]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 3 Trigonometric Functions [Pages 3 - 78]

Q 1 | Page 78

Find the principal and general solutions of the equation tan x = sqrt3

Q 2 | Page 78

Find the principal and general solutions of the equation sec x = 2

Q 3 | Page 78

Find the principal and general solutions of the equation  cot x = -sqrt3

Q 4 | Page 78

Find the general solution of cosec x = –2

Q 5 | Page 78

Find the general solution of the equation cos 4 x = cos 2 x

Q 6 | Page 78

Find the general solution of the equation cos 3x + cos x – cos 2x = 0

Q 7 | Page 78

Find the general solution of the equation sin 2x + cos x = 0

Q 8 | Page 78

Find the general solution for each of the following equations sec2 2x = 1– tan 2x

Q 9 | Page 3

Find the general solution of the equation  sin x + sin 3x + sin 5x = 0

[Pages 81 - 82]

### NCERT solutions for Class 11 Mathematics Textbook Chapter 3 Trigonometric Functions [Pages 81 - 82]

Q 1 | Page 81

Prove that 2 cos  pi/13 cos  (9pi)/13 +  cos  (3pi)/13 + cos  (5pi)/13 = 0

Q 2 | Page 81

Prove that: (sin 3+ sin x) sin + (cos 3– cos x) cos = 0

Q 3 | Page 82

Prove that:  (cos x  + cos y)^2 + (sin x - sin y )^2 =  4 cos^2  (x + y)/2

Q 4 | Page 82

Prove that  (cos x -  cosy)^2 + (sin x -  sin y)^2 = 4 sin^2  (x - y)/2

Q 5 | Page 82

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

Q 6 | Page 82

Prove that ((sin 7x + sin 5x) + (sin 9x + sin 3x))/((cos 7x + cos 5x) + (cos 9x + cos 3x)) = tan 6x

Q 7 | Page 82

Prove that sin 3x + sin 2x – sin x = 4sin x cos  x/2 cos  (3x)/2

Q 8 | Page 82

Find sin x/2, cos x/2 and tan x/2 of the following

tan x =  -4/3, x in quadrant II

Q 9 | Page 82

Find sin x/2, cos x/2 and tan x/2 of the following

cos x =  1/3, x in quadrant III

Q 10 | Page 82

Find sin x/2, cos x/2 and tan x/2 of the following

sin x =  1/4, x in quadrant II

## Chapter 3: Trigonometric Functions ## NCERT solutions for Class 11 Mathematics Textbook chapter 3 - Trigonometric Functions

NCERT solutions for Class 11 Mathematics Textbook chapter 3 (Trigonometric Functions) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 11 Mathematics Textbook chapter 3 Trigonometric Functions are Transformation Formulae, Values of Trigonometric Functions at Multiples and Submultiples of an Angle, Sine and Cosine Formulae and Their Applications, 180 Degree Plusminus X Function, 2X Function, 3X Function, Expressing Sin (X±Y) and Cos (X±Y) in Terms of Sinx, Siny, Cosx and Cosy and Their Simple Applications, Concept of Angle, Introduction of Trigonometric Functions, Signs of Trigonometric Functions, Domain and Range of Trigonometric Functions, Trigonometric Functions of Sum and Difference of Two Angles, Trigonometric Equations, Truth of the Identity, Negative Function Or Trigonometric Functions of Negative Angles, 90 Degree Plusminus X Function, Conversion from One Measure to Another, Graphs of Trigonometric Functions.

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