Mathematics Solution of Trigonometric Functions Online Test

Maan AliLast Updated: October 15, 2025

Important Math Solution of Trigonometric Functions Question and Answer

Total Questions:	70
Time Allowed:	40 Minutes
Total Marks:	70
How to Attempt Test:	Please choose the right Option in MCQ-type question.
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Math Solution of Trigonometric Functions Practice Test Online With Explanation

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Page 1 of 3

1. If tan A = ½ and tan B = 1/3, then the value of A+B i.e tan -1 ½ + tan -1 1/3 is

π/4

π/6

zero

2. cos (α - β) = cos α cos β + sin α sin β is true for all

β – V

α > β

β > α

α > β > 0

3. $Math 14.03$

4. Sine is a periodic function and its period is ________

3π

4π

5. Sec x = tan x is a

Set

Equation

Trigonometric equation

Algebraic equation

6. The solve a trigonometric equation, firstly we find the solution over the interval which is

Domain

Period

None of these

Range

7. A trigonometric equation has _________ solutions

Infinite

Only one

Two

Many

8. If cos⁻¹ 3/5 – sin⁻¹ 4/5 = cos⁻¹ x, then x =

-1

None of these

9. cot⁻¹ xy+1/x–y + cot⁻¹ yz+1/y–z = cot⁻¹ xz+1/x–z =

None of these

-1

10. $Math 14.02$

11. If sin⁻¹ᵃ + sin⁻¹ β 9 sin⁻¹ ϒ = 3π/2 then aβ + aϒ + βϒ is equal to

-3

12. If tan θ + tan (π/3 + θ) + tan (–π/3 + θ) = a tan 3θ, then a =

None of these

1/3

13. Solution set of 2cos θ + √3 = 0 is

Finite

Infinite

None of these

14. The number of points of intersection of the two curves y = 2 sin x and y = 5x² + 2x + 3 is

∞

15. $Math 14.01$

16. If x = tan⁻¹ (1/2), y = tan⁻¹(1/3) then x + y

π/3

π/2

π/4

π/6

17. The range of the function cos 1/3 x is

None of these

[-1, 1]

[- 1/3, 1/3]

[-3, 3]

18. Solve for x, cos x = - √3/2

π/2

π/4

π/3

5π/6

19. The period of tan (x/3) is __________

5π

4π

2π

3π

20. Some time it is necessary to __________ both sides of a trigonometric equation.

Square root

Multiplying

Divide

Square

21. Domain of cos θ is:

Set of real numbers

Set of integers

Set of complex numbers

Set of odd numbers

22. Trigonometric functions are ___________

Continuous

Periodic

None of these

1 – 1

23. If you are looking a high point from the ground, then the angle formed is

Right angle

Angle of depression

Angle of elevation

Horizon

24. Cot⁻¹ x = ?

-Tan⁻¹ x

Tan⁻¹(1/x)

1/tan⁻¹x

Cos⁻¹ x

25. tan (-135°) = ________ 0

Page 2 of 3

26. For m ≠ n if tan m θ = tan n θ, then the different values of θ are in

A.P

H.P

G.P

No particular sequence

27. If θ and Ø are the roots of the equation 8x² + 22x + 5 = 0, then

Both sec⁻¹ θ and sec⁻¹ Ø are real

Both tan⁻¹ θ and tan⁻¹ Ø are real

Both sin⁻¹ θ and sin⁻¹ Ø are real

None of these

28. If Cos θ = 0, Then θ =

(2n+1) π/2

(n ± 1) π/2

(2n – 1) π/2

nπ/2

29. The general solution of the equation 1 + cos x = 0 is

{π/2+ 2nπ}

{π + 2nπ}

{-π/2+ 2nπ}

{-π+ 2nπ}

30. Solution of the equation cot⁻¹ x + sin⁻¹ 1/√5 = π/4 is

None of these

x = 0

x = 3

x = 1/√5

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

2nπ = B

nπ + (-1)ⁿ B

nπ + B

2nπ – B

32. If x = tan⁻¹ 1/7 and y = tan⁻¹ 1/3, then

None of these

Cos 3 y = sin 4x

Cos 4y = cos 2 x

Cos 2x = sin 4y

33. 2 π + θ will have terminal side in Quad/
math

III

34. cos (tan⁻¹ ∞) = ?

π/3

π/2

∞

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

60°

75°

30°

45°

36. If sin A = sin β and cos A = cos β, then

A = 2n π + β, n natural number

A = ± β

A = 2n π + β, n is any integer

A = β

37. Solution of 1 + cosx = 0 is

2 π

π/2

None of these

38. The solution of sin²x = ¾ is

None of these

π/3, 2π/3

-π/3, 2π/3

4π/3, 5π/3

39. If θ = 60° then

Sec θ = 4

sin θ = ½

θ = π/4

tan θ = cot 30°

40. Trigonometric equations have solutions due to periodicity of trigonometric functions:

Finite number of

In finite

None of these

Zero

41. If sin x + cos x = 1/5, 0 ≤ x ≤ π then tan x is equal to

– 4/3 or –3/4

4/5

4/3

None of these

42. If sin x = ½ , then x =

π/6, 5π/6

- π/6, 5π/6

- π/6, -5π/6

π/3, 2π/3

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

nπ

nπ + π/4

nπ ± π/4

nπ/3 + π/12

44. Tangent is a periodic function and its period is __________

3π

4π

2π

45. tan⁻¹ x > cot⁻¹ x holds for

x < 1

All values of x

x > 1

x = 1

46. If five triangles are constructed having sides of the lengths indicated below, the triangle that will NOT be a right triangle is:

5, 12, 13

12, 15, 18

3, 4, 5

8, 15, 17

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

One real solution

More than one real solution

None of these

No solution

48. Cosec⁻¹ x + sec⁻¹ x

π/6

π/2

3π/4

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

π/6, π/9

π/3, π/9

π/9, π/4

π/3, π/4

50. Distance between A (3, 8), B(5, 6) is :

√8

√5

√3

√2

Page 3 of 3

51. Area of ∆ABC =

½ ac Sin β

ab Sin a

½ ab Sin a

½ ac Sin ϒ

52. Tan 75° - cos 75° is equal to

2 = √3

2-√3

2√3

53. $Math 14.04$

54. sec (-360°) = _________

55. The value of cos 15° -sin 15° is

1/2√2

1/√2

-1/√2

56. Solution of the equation sec θ – cosec θ = 4/3 is

θ = nx/2 + (– 1)ⁿ/2 sin⁻¹ 3/4

θ = n π + (– 1)ⁿ sin⁻¹ 3/4

None of these

θ = n π ± sin⁻¹ (3/4)

57. Domain of sin θ is

Set of complex numbers

Set of natural numbers

Set of real numbers

Set of even numbers

58. Tan 3x tan 2x – tan x is equal to:

None of these

-tan x tan 2x tan 3x

Tan x tan 2x tan 3x

Tan x tan 2x – tan x tan 3x – tan 2x tan 3x

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

2nπ ± π/3

nπ ± π/3

nπ ± π/6

2nπ ± π/6

60. If 1 + cos x = 0 then solution set is

{π + 2nπ}

{π + 3nπ}

{π + 2n}

{2nπ}

61. The equations containing at least one trigonometric function are called.

Algebraic equation

Trigonometric equation

Trigonometric sentence

Algebraic sentence

62. Sin⁻¹ (1) + cos⁻¹ (1) = ?

π/2

-1

π/4

63. Which one is a pair of allied angles:

(180° + θ)

None of these

(180° – θ, 180° + θ)

(180° – θ)

64. cos x = ½ has a solution

π/3

π/4

π/6

π/2

65. $Math 14.05$

66. If sin x + cos x = 0, then x =

–π/4, 3π/4

None of these

–π/4, – π/2

π/4, – π/4

67. The number of solutions of the equation |cot x| = cot x + 1/sin x [0 ≤ x ≤ 2 π] is

68. Sec⁻¹ (x) = ?

Cos⁻¹ x

(sec x)⁻¹

None of these

Cos⁻¹(1/x)

69. Sin (2π – θ)

Tan θ

Cos θ

Sin θ

-sin θ

70. Tan 1°tan 2°tan 3°tan 4° ….. tan 87°tan 88 tan 89° is equal to

∞

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Maan AliLast Updated: October 15, 2025

Important Math Solution of Trigonometric Functions Question and Answer

Math Solution of Trigonometric Functions Practice Test Online With Explanation

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