Roll No.

: Time -
Date : MM - 112  

1. 1
What is the value of sin .

2. Find the value of sin 75° cos 15° + cos 75° sin 15° 1

3. Express the following as sum or difference : cos 5θ cos 3θ 1

4. Express each of the following as a product : sin 32° + sin 54° 1

5. 2
Find the value .

6. 2
Solve the equation .

7. Evaluate, sin 105° + cos 105°. 2

8. 2
Find the value of .

9. 2
What is the value of

10. A train is travelling on a curve of 700 m radius at 14 km/h, Through what angle will it turn in one 2
minute ?

11. If the angular diameter of the moon be 30′, how far from the eye a coin of diameter 2.2 cm be 2
kept to hide the moon ?

12. Find the value of the following : tan (– 1125°) 2

13. In triangle ABC, prove that : cos (A + B) + cos C = 0. 2

14. 2
In triangle ABC, prove that :

15. In quadrilateral ABCD, prove that : cos (A + B) = cos (C + D). 2

16. 2
Find the principal solution of the equation: sin x =

17. 2
Find the principal solution of the equation: cos x = .
18. 4
If sin x = , cos y = and x, y both lie in the second quadrant, find the values of sin (x + y)

19. 4
Prove that .

20. Solve the equation cos 3x = sin 2x 4

21. 4
In ΔABC, prove that .

22. 4
In ΔABC, prove that .

23. 4
Prove that, cos 20° cos 40° cos 60° cos 80° = .

24. Solve for x : tan2 x + cot2 x = 2 4

25. Solve the equation for general solution 2 sin2 x + sin2 2x = 2. 4

26. Solve : 2 cos2 x + 3 sin x = 0. 4

27. 4
Prove the following identitie :

28. Find the general solution of the equation : 2 tan x – cot x + 1 = 0 4

29. Find the general solution of the equation : cot2 x + 3 cosec x + 3 = 0 4

30. tan2x + (1 – )tan x – =0 4

31. 4
In ΔABC, prove that :

32. 4
In ΔABC, prove that :

33. 4
In ΔABC, prove that :

34. Find the general solution of the equation, 2 sin x + cos x = 1 + sin x. 6

35. In ΔABC, prove that : a3 sin (B – C) + b3 sin (C – A) + c3 sin (A – B) = 0 6

36. 6
+ .