Trigonometry (Railway Maths) (Part – III)

Total Questions: 50

31. If sinθ + cosecθ = 2, then the value of sin⁸θ + cosec⁸θ is: [RRB NTPC 18/01/2021 (Morning)]

Correct Answer: (a) 2
Solution:

32. In right angle ΔABC, right angled at B, if tan A = √3, then sinA cosC + cosA sinC = ? [RRB NTPC 18/01/2021 (Morning)]

Correct Answer: (a) 1
Solution:

33. The value of cos75° + sin15° is equal to: [RRB NTPC 18/01/2021 (Evening)]

Correct Answer: (a) (√3 − 1) / √2
Solution:

34. In a triangle, right angled at B, AB = 12 cm and BC = 5 cm. What will be the value of ? [RRB NTPC 18/01/2021 (Evening) ]

(i) sinAcosA
(ii) sinCcosC

Correct Answer: (c) 60/169, 60/169
Solution:

35. Answer the following question? [RRB NTPC 18/01/2021 (Evening) ]

Correct Answer: (b) 9/2
Solution:

36. If sinA = 1/2 and cosB = 1/2, then find A + B. [RRB NTPC 19/01/2021 (Morning)]

Correct Answer: (b) 90°
Solution:

SinA = 1/2 = sin30°
⇒ A = 30°
⇒ CosB = 1/2 = cos60°
B = 60°
⇒ A + B = 90°

37. The value of 1 − sin35° cos55° is equal to: [RRB NTPC 19/01/2021 (Evening)]

Correct Answer: (c) Cos²35°
Solution:

1 − sin35° cos55°
= 1 − sin35° cos(90° − 35°)
= 1 − sin35° sin35°
= 1 − (sin²35°) = cos²35°

38. If tan2θ = cot(θ + 6°), then θ is: [RRB NTPC 19/01/2021 (Evening)]

Correct Answer: (c) 28°
Solution:

tan2θ = cot(θ + 6°)
tan2θ = tan[90° − (θ + 6°)]
2θ = 84° − θ
⇒ 3θ = 84°
⇒ θ = 28°

39. If A + B = 90° and sinA = 3/5, then the value of tanB is: [RRB NTPC 20/01/2021 (Morning)]

Correct Answer: (d) 4/3
Solution:A + B = 90°, and sin A = 3/5,
Then, the value of tanB is = 4/3

40. If sin30° = cos(θ − 6°), then θ is: [RRB NTPC 20/01/2021 (Evening)]

Correct Answer: (a) 24°
Solution:

sin30 = cos(θ − 6°)
⇒ sin30 = sin(90° − θ + 6°)
⇒ 30 = 96° − θ
⇒ θ = 24°