Trigonometry (Railway Maths) (Part – IV)

Total Questions: 50

11. What is the value of the following expression? [RRB NTPC 31/01/2021 (Evening)]

(cos3x + cosx) / (sin3x − sinx)

Correct Answer: (d) cotx
Solution:

12. If sin(A − B) = 1/2 and cos(A + B) = 1/2, with 0° B, then find the measure of A and B. [RRB NTPC 01/02/2021 (Morning)]

Correct Answer: (a) 45°, 15°
Solution:

sin(A − B) = 1/2 = sin30° -------- (i)
cos(A + B) = 1/2 = cos60° -------- (ii)
From equation (i) and (ii)
(A − B) = 30°, (A + B) = 60°
A = 45° and B = 15°

13. If (1 + tanA)(1 + tanB) = 2, then what will be the value of tan(A + B)? [RRB NTPC 02/02/2021 (Morning)]

Correct Answer: (d) 1
Solution:

We know that if,
(1 + tanA)(1 + tanB) = 2 then A + B = 45°
tan(A + B) = tan45° = 1

14. The value of (tan45° − tan30°) / (1 + tan45° tan30°) is: [RRB NTPC 02/02/2021 (Morning)]

Correct Answer: (b) 2 − √3
Solution:

15. If cosθ + secθ = √3, then the value of cos³θ + sec³θ is: [RRB NTPC 02/02/2021 (Evening) ]

Correct Answer: (d) 0
Solution:

cosθ + secθ = √3
(cos³θ + sec³θ) = (√3)³ − 3√3 = 0

16. If cot3θ cot6θ = 1, then the value of tan 15θ will be: [RRB NTPC 03/02/2021 (Morning) ]

Correct Answer: (c) -1/ √3
Solution:

If cotx × coty = 1, then x + y = 90°
cot3θ · cot6θ = 1
⇒ 3θ + 6θ = 90°
⇒ 9θ = 90°
⇒ θ = 10°
Now,
tan150 = tan150° = tan(90° + 60°)
= −cot60° = −1/√3

17. Answer the following question? [RRB NTPC 03/02/2021 (Morning) ]

Correct Answer: (d) 2
Solution:

18. The minimum value of 11 sin²θ + 12cos²θ is: [RRB NTPC 04/02/2021 (Morning) ]

Correct Answer: (c) 11
Solution:

For Minimum value Put θ = 90° then
11 sin²θ + 12 cos²θ = 11 sin²90° + 12 cos²90°
= 11 + 0 = 11

19. In triangle ABC , what will be the value of a(bcosC - ccosB) ? [RRB NTPC 05/02/2021 (Morning) ]

Correct Answer: (d) b² - c²
Solution:

20. Find the value of cos37°sec143° + sin34°cosec146°? [RRB NTPC 08/02/2021 (Morning) ]

Correct Answer: (d) 0
Solution: