ECAT Mathematics Inverse Trigonometric Functions Online Test

1. Tan⁻¹ 1/7+ Tan⁻¹ 1/13 =

2. If (1 + tan θ)(1 + tan Ø) = 2, then θ + Ø =

3. Range of Tan⁻¹ x is

4. The solution of the equation cos² θ + sin θ + 1 = 0 lies in the interval

5. If 2 tan⁻¹ (cos x) = tan⁻¹ (cosec² x), then x is equal to

6. One root of the equation cos x – x + ½ = 0 lies in the interval

7. The general solution of tan 3x = 1 is

8. The general solution of sin x – 3 sin 2x + sin 3x = cos x – 3 cos 2x + cos 3x is

9. Inverse of sin function is written as

10. Tan⁻¹(1) =

11. The solution set of the system of equation: x – y = 2π/3, cos x + cos y = 2/3, where x and y are real in:

12. Which of the following is solution of cos 3x = ½ = ?

13. The value of sin [arc cos (- ½ )]is

14. For n ϵ Z, the general solution of the equation (√3 – 1)sin θ + (√3 + 1) cos θ = 2 is

16. If 5 cos 2 θ + 2 cos² θ/2 + 1 = 0, - π < θ < π, then θ =

17. The number of solutions of the equation tan x + sec x = 2 cos lying the interval [0, 2π] is

19. Tan⁻¹ 1/7 + Tan⁻¹ 1/13 =

20. If sin A = sin B, cos A = cos B, then the value of A in terms of B is

21. If 4 sin² θ = 1, then values of θ are

22. Tan⁻¹ (2A/1 – A²) =

23. Range of cosec⁻¹x is

24. The principal tangent function is

25. 2Cos⁻¹ A =

26. tan⁻¹(1/4) + tan⁻¹(2/9) is equal to

27. The values of θ satisfying sin 7 θ = sin 4 θ – sin θ and 0 < θ < π/2 are

28. The value of cos [cos⁻¹ (- √3/2) + π/6] is

29. Tan⁻¹(3A – A³/1 – 3A²)

30. Tan⁻¹ ½ + Tan⁻¹ 1/13 =

31. cot θ = sin 2 θ (θ ≠ nπ, n integer) if θ =

32. The smallest positive root of the equation tan x – x = 0 lies on

34. The domain of principal sine function is

35. Sin⁻¹{2A√1 – A²}

36. The number of values of x in the interval [0, 5π] satisfying the equation 3 sin² x – 7 sinx + 2 = 0 is

39. Tan⁻¹ A – Tan⁻¹ B =

40. Tan⁻¹ A + Tan⁻¹ B =

41. General solution of tan 5 θ = cot 2 θ is

42. If sin⁻¹ x = π/5 for some x ϵ (-1,1), then the value of cos⁻¹x is

43. If sin 6 θ + sin 4 θ + sin 2 θ = 0, then θ =

44. The set of values of x for which tan3x–tan2x/1+tan3xtan2x = 1 is

45. The principal cosine function is

46. The graph of y = sin⁻¹ x is along the

47. The domain of the function y = cos⁻¹ x is

48. The value of sin (Cos⁻¹√3/2) is

49. Tan⁻¹(– 1) =

50. The domain of principal cosine function is

51. Tan⁻¹(x – 1/x – 2) + Tan (x + 1/x + 2) =

52. Tan⁻¹ 1/3 + Tan⁻¹ 1/5 + Tan⁻¹ 1/7 + Tan⁻¹ 1/8

53. Tan⁻¹ A + Tan⁻¹ (1–A/1+A)

54. Tan⁻¹ A + Tan⁻¹ B + Tan⁻¹ C =

55. The equation 2 cos²(x/2) sin²x = x² + 1/x² 0 ≤ x ≤ π/2 has