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NCERT solutions Mathematics Class 11 chapter 3 Trigonometric Functions

Chapters

NCERT Mathematics Class 11

Mathematics Textbook for Class 11

Chapter 3 - Trigonometric Functions

Pages 54 - 55

Find the radian measures corresponding to the following degree measures:

25°

Q 1.1 | Page 54

Find the radian measures corresponding to the following degree measures:

– 47° 30

Q 1.2 | Page 54

Find the radian measures corresponding to the following degree measures:

240°

Q 1.3 | Page 54

Find the radian measures corresponding to the following degree measures:

520°

Q 1.4 | Page 54

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

`11/16`

Q 2.1 | Page 55

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

-4

Q 2.2 | Page 55

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

`(5pi)/3`

Q 2.3 | Page 55

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

`(7pi)/6`

Q 2.4 | Page 55

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

Q 3 | 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 4 | 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 5 | 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 6 | 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 7.1 | 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

15 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

21 cm

Q 7.3 | Page 55

Page 63

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

Q 1 | Page 63

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

Q 2 | Page 63

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

Q 3 | Page 63

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

Q 4 | Page 63

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

Q 5 | Page 63

Find the value of the trigonometric function sin 765°

Q 6 | Page 63

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

Q 7 | Page 63

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

Q 8 | Page 63

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

Q 9 | Page 63

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

Q 10 | Page 63

Pages 73 - 74

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

Q 1 | Page 73

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

Q 2 | Page 73

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

Q 3 | Page 73

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

Q 4 | Page 73

Find the value of:  sin 75°

Q 5.1 | Page 73

Find the value of: tan 15°

Q 5.2 | 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 6 | Page 73

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

Q 7 | Page 73

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

Q 8 | Page 73

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

Q 9 | Page 73

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

Q 10 | Page 73

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

Q 11 | Page 73

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

Q 12 | Page 73

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

Q 13 | Page 73

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

Q 14 | Page 73

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

Q 15 | Page 73

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

Q 16 | Page 73

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

Q 17 | Page 73

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

Q 17 | Page 73

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

Q 18 | Page 73

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

Q 19 | Page 73

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

Q 20 | Page 73

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

Q 21 | Page 73

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

Q 22 | Page 74

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

Q 23 | Page 74

Prove that cos 4x = 1 – 8sincosx

Q 24 | Page 73

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

Q 25 | Page 74

Pages 3 - 78

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

Q 1 | Page 78

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

Q 2 | Page 78

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

Q 3 | Page 78

Find the general solution of cosec x = –2

Q 4 | Page 78

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

Q 5 | Page 78

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

Q 6 | Page 78

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

Q 7 | Page 78

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

Q 8 | Page 78

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

Q 9 | Page 3

Pages 81 - 82

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

Q 1 | Page 81

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

Q 2 | Page 81

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

Q 3 | Page 82

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

Q 4 | Page 82

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

Q 5 | Page 82

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

Q 6 | Page 82

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

Q 7 | 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 8 | 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 9 | Page 82

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

`sin x =  1/4`, x in quadrant II

Q 10 | Page 82

NCERT Mathematics Class 11

Mathematics Textbook for Class 11
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