# NCERT Solutions for Class 11 Maths

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# Trigonometric Functions

1.    Find the radian measures corresponding to the following degree measures:

(i) 25°

(ii) -47° 30′

(iii) 240°

(iv) 520°

2.    Find the degree measures corresponding to the following radian measures

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

4.    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

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.

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

7.    Find the angle in radians 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

Exercise 2

Find the values of other trigonometric functions in exercises 8 to 12.

Find the values of the trigonometric functions in exercises 13 to 17.

13.   sin 765°

14.   cos ec(-1410)°

15.

16.

17.

Exercise 3

18.

19.

20.

21.

22.   Find the value of:

(i) sin 75°

(ii) tan 15°

Prove the following:

23.

24.

25.

26.

27.    sin(n + 1)xsin (n + 2)x + cos(n + 1)xcos(n + 2)x = cosx

28.

29.   sin2 6x – sin2 4x = sinxsin 10x

30.   cos22x – cos26x = sin4xsin8x

31.   sin2x + 2sin4x + sin6x = 4cos2 xsin4x

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

33.

34.

35.

36.

37.

38.

39.   cot x cot 2x – cot 2x cot 3x – cot 3x cot x = 1

40.

41.   cos 4x = 1 – 8 sin2 x cos2 x

42.   cos 6x = 32 cos6 x – 48 cos4 x + 18 cos2 x – 1

Exercise 4

Find the principal and general solutions of the following equations:

43.   tan x = √3

44.   sec x = 2

45.   cot x = -√3

46.   cos ec x = -2

47.   cos 4x = cos 2x

48.   cos 3x + cos x – cos 2x = 0

49.   sin 2x + cosx = 0

50.   sec2 2x = 1 – tan 2x

51.   sin x + sin 3x + sin 5x = 0

Exercise 5

Prove that:

52.

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

54.

55.

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

57.

58.

Find  in each of the following:

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