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SSC CHSL 2025 · PYQ · Trigonometry · medium

Simplify: (sin(x) + cos(x))² / (1 + sin(x)cos(x))

Answer

The correct answer is A: (1 + 2sin(x)cos(x)) / (1 + sin(x)cos(x)). (sinx + cosx)² = 1 + 2sinx·cosx. So the expression = (1 + 2sinx·cosx)/(1 + sinx·cosx).

  1. A.(1 + 2sin(x)cos(x)) / (1 + sin(x)cos(x))✓ Correct
  2. B.(7 + 8sin(x)cos(x)) / (3 + sin(x)cos(x))
  3. C.(9 + 2sin(x)cos(x)) / (7 + sin(x)cos(x))
  4. D.(6 + 5sin(x)cos(x)) / (1 + sin(x)cos(x))

Explanation

(sinx + cosx)² = 1 + 2sinx·cosx. So the expression = (1 + 2sinx·cosx)/(1 + sinx·cosx).
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