If 2 Cot x = 5, then what is (2 Cos x - Sin x) / (2 Cos x + Sin x) equal to?
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.
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