Class 10 Trigonometry त्रिकोणमिति MCQs Questions 2026

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📅 28/12/2025

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Class 10 Trigonometry त्रिकोणमिति MCQs Questions 2026
1.
If θ = 45°, then sin θ + cos θ =

A. √2
B. 1/√2
C. 1/2
D. 1

2. sin²75° + sin²15° =

A. 0
B. 1
C. −1
D. 2

3. If tan θ = p/q, then (p sin θ − q cos θ) / (p sin θ + q cos θ) =

A. p² − q²
B. (p² + q²)/(p² − q²)
C. (p² + q²)/2
D. (p² − q²)/(p² + q²)

4. cos 48° − sin 42° =

A. 1
B. 0
C. 2
D. −1

5. (1 − tan²45°)/(1 + tan²45°) =

A. sin 190°
B. sin 0°
C. tan 90°
D. sin 45°

6. If tan 35° × tan 55° = sin A, then A =

A. 35°
B. 55°
C. 90°
D. 45°

7. 1/sin θ =

A. 1
B. cosec θ
C. sec θ
D. cot θ

8. If sec θ + tan θ = x, then tan θ =

A. (x² + 1)/2x
B. (x² − 1)/2x
C. x/(x + 1)
D. (x² − 1)/x

9. cos1° · cos2° · cos3° … cos90° =

A. 0
B. 1
C. −1
D. √2

10. 1 + cot²θ =

A. cot²θ
B. sin²θ
C. cosec²θ
D. cos²θ

11. sin²θ + 1/(1 + tan²θ) =

A. 1
B. 1/2
C. 0
D. 2

12. If 2 sin α = 2, then α =

A. 0°
B. 45°
C. 60°
D. 90°

13. sec 11° / cosec 79° =

A. 1
B. 0
C. 2
D. −1

14. If a sin θ = 1 and b cos θ = 1, then tan θ =

A. a/b
B. b/a
C. 1
D. a/b²

15. tan45° : tan60° =

A. 1 : 2
B. 3 : 1
C. 1 : √3
D. √3 : 1

16. If cos θ = √3/2, then θ =

A. 60°
B. 30°
C. 45°
D. 90°

17. 2(sin²α + cos²α) =

A. 1
B. 0
C. 2
D. −1

18. If cot θ = 1/√3, then sec θ =

A. √3
B. 1/2
C. 2
D. 1/√3

19. If tan θ = 4/3, then sin θ + cos θ =

A. 7/3
B. 7/4
C. 7/5
D. 5/7

20. cosec²57° − tan²33° =

A. 0
B. 1
C. −1
D. 2

21. If θ = 30°, then 2cos2θ =

A. 1
B. 2
C. √3
D. √2

22. 1/√3 is equal to

A. sin30°
B. tan30°
C. cos60°
D. sin45°

23. (cos37°/sin53°) + (cot34°/tan56°) =

A. 1
B. 2
C. 0
D. −1

24. If tan θ = 12/5, then sin θ =

A. 5/12
B. 12/13
C. 5/13
D. 12/5

25. (cosec θ − cot θ)² =

A. (1 + cosθ)/(1 − cosθ)
B. (1 − cosθ)/(1 + cosθ)
C. (1 + sinθ)/(1 − sinθ)
D. sinθ cosθ

26. cosec²θ − cot²θ =

A. 0
B. 1
C. −1
D. 2

27. If √3 tan2θ − 3 = 0, then θ =

A. 15°
B. 30°
C. 45°
D. 60°

28. If sin θ = √3/2, then cosec θ + cot θ =

A. 2 + √3
B. 2√3
C. √2
D. √3

29. Which of the following is true?

A. sin30° = tan30°
B. sin30° = cos30°
C. sin30° = cos60°
D. sin30° = tan60°

30. (1 + cot²θ)(1 − cos²θ) =

A. 1
B. sin²θ
C. tan²θ
D. cos²θ

31. If θ and φ are complementary angles, then

A. cosθ = cosφ
B. secθ = cosecφ
C. sinθ = sinφ
D. tanθ = tanφ

32. sec B × cos B =

A. 2
B. −1
C. 0
D. 1

33. (cos59°/sin31°) × (tan80°/cot10°) =

A. 1/√2
B. √3/2
C. 1
D. 1/2

34. If sinθ = cosθ (0° ≤ θ ≤ 90°), then θ =

A. 30°
B. 45°
C. 60°
D. 90°

35. 5cosec²θ − 5cot²θ =

A. 1
B. 5
C. −5
D. 0

36. sec²10° − cot²80° =

A. 1
B. 0
C. 3/2
D. 1/2

37. tan10° tan15° tan75° tan80° =

A. 1/√3
B. 0
C. 1
D. √2

38. If 3α = 180°, then cos α =

A. 0
B. 1
C. 1/2
D. 1/√2

39. (sin30° + cos45° − tan60°) / (cot30° − sin45° − cos60°) =

A. −1
B. 2
C. 3
D. 4

40. sin70° + sin20° + cos70° =

A. 1
B. 2
C. 0
D. −1

41. tan A = ?

A. cot (90° − A)
B. sec (90° − A)
C. cosec (90° − A)
D. cos (90° − A)

42. sec² A/(1 + cot² A) = ?

A. sec² A
B. cosec² A
C. cot² A
D. tan² A

43. (cos 60° + 1)/(cos 60° − 1) = ?

A. 2
B. −2
C. 3
D. −3

44. यदि A + B = 90°, तो tan A = ?

A. cot B
B. tan B
C. sec B
D. cosec B

45. 8 sec² θ − 8 tan² θ = ?

A. 16
B. 9
C. 8
D. 0

46. (2 sin 38°)/cos 52° = ?

A. 2
B. 1
C. 3
D. 4

47. cos (90° – θ) का मान है—

A. sin θ
B. −sin θ
C. cos θ
D. −cos θ

48. tan 30° sin 30° cot 60° cosec 30° = ?

A. 1/√3
B. √3
C. 1/(2√3)
D. 1/3

49. यदि θ = 45°, तो tan² θ + 1/sin² θ = ?

A. 1
B. 2
C. 3
D. 4

50. यदि tan θ = 5/12, तो sec² θ = ?

A. 169/144
B. 144/169
C. 25/144
D. 169/25

51. sin 18°/cos 72° = ?

A. 1/2
B. 1
C. √3/2
D. 0

52. sin² 37° + sin² 53° = ?

A. 0
B. 1
C. −1
D. 2

53. √((1 − cos θ)/(1 + cos θ)) = ?

A. sec θ − tan θ
B. cos θ − sin θ
C. cosec θ − cot θ
D. tan θ − cot θ

54. यदि 15 cot A = 8, तो sin A = ?

A. 15/8
B. 17/15
C. 15/17
D. 8/15

55. 1 + tan² θ = ?

A. sec² θ
B. cosec² θ
C. tan² θ
D. cot² θ

56. यदि tan θ = 12/5, तो sin θ = ?

A. 5/12
B. 12/13
C. 5/13
D. 12/5

57. यदि sin θ = 4/5, तो cosec θ = ?

A. 5/4
B. 4/5
C. 5/3
D. 3/4

58. 9 sec² A − 9 tan² A = ?

A. 1
B. 9
C. 8
D. 0

59. यदि tan θ = 15/8, तो sin θ = ?

A. 8/17
B. 8/15
C. 15/17
D. 17/8

60. (1 + cot² A)/(1 + tan² A) = ?

A. sec² A
B. cosec² A
C. cot² A
D. tan² A

61. cos (90° − θ) = ?

A. cos 90° + cos θ
B. sin θ
C. −sin θ
D. −cos θ

62. यदि sec θ = 2, तो cos θ = ?

A. 1/2
B. 2
C. √3/2
D. −1/2

63. sin 63°/cos 27° = ?

A. √3
B. 1
C. 2
D. 3

64. (1 + tan θ + sec θ)(1 + cot θ − cosec θ) = ?

A. 0
B. 1
C. 2
D. −1

65. यदि sin A = 3/5 और A एक न्यून कोण है, तो tan A = ?

A. 3/4
B. 4/3
C. 5/3
D. 3/5

66. यदि tan θ = √3, तो sec θ = ?

A. 2
B. √3
C. 1
D. 1/2

67. यदि cos 32° = x और cos 58° = y, तो—

A. x > y
B. x = y
C. x < y
D. इनमें से कोई नहीं

68. यदि tan A = 1/√3, तो A = ?

A. 15°
B. 30°
C. 45°
D. 60°

69. sin 38° − cos 52° = ?

A. 0
B. 1
C. √3/2
D. −1

70. cosec² θ के बराबर है—

A. (1 − cos² θ)/(1 + cos² θ)
B. (1 + tan² θ)/(1 + cot² θ)
C. (sin² θ + cos² θ)/(1 − cos² θ)
D. (sin² θ + cos² θ)/(1 − sin² θ)

71. यदि tan θ = √3, तो θ = ?

A. 90°
B. 45°
C. 30°
D. 60°

72. यदि (tan θ + cot θ) = 6, तो tan² θ + cot² θ = ?

A. 25
B. 27
C. 24
D. 34

73. 1/√3 किसके बराबर है?

A. sin π/3
B. 6 cot π/3
C. tan π/6
D. cos π/6

74. यदि √3 sec θ = 2, तो θ = ?

A. 0°
B. 30°
C. 45°
D. 60°

75. (2 sin² 63° + 1 + 2 sin² 27°)/(3 cos² 17° − 2 + 3 cos² 73°) = ?

A. 3/2
B. 2/3
C. 2
D. 3

76. sin (90° − θ) = ?

A. cos θ
B. sin θ
C. tan θ
D. −cos θ

77. sin² 48° − cos² 42° = ?

A. 0
B. 1
C. −1
D. 2

78. यदि cos A = 4/5 है, तो sin A = ?

A. 3/5
B. 5/4
C. 4/3
D. 1/5

79. tan 60° का मान है—

A. 1/3
B. √3
C. 1/√3
D. 3√3

80. यदि sec θ + tan θ + 1 = 0, तो sec θ − tan θ = ?

A. 1
B. −1
C. 0
D. 2

81. (2 tan 30°)/(1 + tan² 30°) = ?

A. sin 60°
B. cos 60°
C. tan 60°
D. sin 30°

82. यदि 2 cos θ = √3, तो θ = ?

A. 45°
B. 60°
C. 30°
D. 90°

83. sin² A + cos² A = ?

A. 1
B. 0
C. sec² A
D. tan² A

84. (cos 60° + 1)/(cos 60° − 1) = ?

A. −2
B. −3
C. 3
D. 2

85. यदि tan θ = 8/15, तो cosec θ = ?

A. 17/8
B. 8/17
C. 15/17
D. 17/15

Bihar Board Class 10 Trigonometry त्रिकोणमिति Exam 2026 MCQs Questions Answer Key

Q. No.AnsQ. No.AnsQ. No.AnsQ. No.Ans
1A23B45C67A
2B24B46A68B
3D25B47B69A
4B26B48D70C
5B27B49C71D
6C28D50A72D
7B29C51B73C
8B30A52B74B
9A31B53C75D
10C32D54C76A
11A33C55A77A
12D34B56B78A
13A35B57A79B
14B36A58B80B
15C37C59C81A
16B38C60C82C
17C39A61B83A
18C40*62A84B
19C41A63B85A
20B42D64C
21A43D65A
22B44A66A
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