Trigonometry (Railway Maths) (Part – IV)

Total Questions: 50

1. If tan3θ · tan60° = 1, then the value of tan30 θ is: [RRB NTPC 23/01/2021 (Morning)]

Correct Answer: (b) −√3
Solution:

tan3θ tan6θ = 1
⇒ 3θ + 6θ = 90° ⇒ 9θ = 90° ⇒ θ = 10°
Now, tan300 = tan300° = tan(270° + 30°)
= −cot30° = −√3

2. If 2 sin(3x − 3)° = tan240°, then the value of x in degree is: [RRB NTPC 23/01/2021 (Morning)]

Correct Answer: (a) 21°
Solution:

2 sin(3x − 3)° = tan240°
⇒ 2 sin(3x − 3)° = tan(180° + 60°)
⇒ 2 sin(3x − 3)° = tan60°
⇒ 2 sin(3x − 3)° = √3
⇒ sin(3x − 3)° = √3 / 2
⇒ sin(3x − 3)° = sin60°
⇒ (3x − 3)° = 60°
⇒ 3x = 63°
⇒ x = 21°

3. If cos(x − y) = √3/2 and sin(x + y) = 1, where x and y are positive acute angles and x ≥ y, then x and y are _______: [RRB NTPC 25/01/2021 (Evening)]

Correct Answer: (d) 60°, 30°
Solution:

4. If 1 + tanθ = √3, then find the value of √3 cotθ − 1 ? [RRB NTPC 25/01/2021 (Evening) ]

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

5. If x + y = 75 and sin x : sin y = (1/√2) : (1/2), then x : y is: [RRB NTPC 28/01/2021 (Evening)]

Correct Answer: (d) 3 : 2
Solution:

6. cos²31° + cos²59° is equal to: [RRB NTPC 28/01/2021 (Evening)]

Correct Answer: (c) 1
Solution:

7. If sinθ + cosecθ = √5, then the value of sin³θ + cosec³θ is: [RRB NTPC 28/01/2021 (Evening)]

Correct Answer: (d) 2√5
Solution:

8. If cot35° = 2 − √3, then the value of tan35° cot55° + tan55° cot35° is: [RRB NTPC 29/01/2021 (Evening)]

Correct Answer: (d) 14
Solution:

9. Find the value of tan1° · tan2° · tan3° · … · tan89°. [RRB NTPC 30/01/2021 (Morning)]

Correct Answer: (b) 1
Solution:

10. If sinx − 3cosx = √3 cosx, then the value of cotx is: [RRB NTPC 31/01/2021 (Morning)]

Correct Answer: (d) (3 − √3) / 6
Solution: