Question
If 2 Cot x = 5, then what is (2 Cos x - Sin x) / (2 Cos x + Sin x) equal to?
This question was previously asked in
SSC CGL 2023 (Tier-II) Paper 1 Previous Year Paper (26-Oct-2023) (Shift-1)
The correct answer is
2/3
2 cot x = 5 ⇒ cot x = 5/2 = cos x / sin x.
Let sin x = 2k ⇒ cos x = 5k (by ratio).
Use identity: sin²x + cos²x = 1 ⇒ (2k)² + (5k)² = 1 ⇒ 4k² + 25k² = 1 ⇒ 29k² = 1 ⇒ k² = 1/29.
Now plug into expression:
(2×5k − 2k)/(2×5k + 2k) = (10k − 2k)/(10k + 2k) = 8k/12k = 2/3.
Was this answer helpful?
Need Expert Advice?
Upcoming Exams
Test Series
SSC
SSC CGL (Tier I + Tier II) 2026 Mock Test Series - Latest Pattern
2500 Tests 6 Tests Free
3990 Attempts
4.2(838)
English, Hindi
More Questions from SSC CGL
