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SSC CHSL 2025 · PYQ · Trigonometry · medium

If tan(x) + cot(x) = 2, find sin(x) cos(x).

Answer

The correct answer is D: 1/2. tan x + cot x = sin x/cos x + cos x/sin x = (sin²x + cos²x)/(sin x cos x) = 1/(sin x cos x) = 2. Therefore sin x cos x = 1/2.

  1. A.6/7
  2. B.1
  3. C.7/9
  4. D.1/2✓ Correct

Explanation

tan x + cot x = sin x/cos x + cos x/sin x = (sin²x + cos²x)/(sin x cos x) = 1/(sin x cos x) = 2. Therefore sin x cos x = 1/2.
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