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SSC CHSL 2023 · PYQ · Trigonometry · medium

cosθ/(secθ−1) + cosθ/(secθ+1) is equal to:

Answer

The correct answer is A: 2cot²θ. cosθ/(secθ−1) + cosθ/(secθ+1) = cosθ[(secθ+1+secθ−1)/((secθ)²−1)] = cosθ[2secθ/tan²θ] = cosθ×(2/cosθ)×(cos²θ/sin²θ) = 2cos²θ/sin²θ = 2cot²θ.

  1. A.2cot²θ✓ Correct
  2. B.2cos²θ
  3. C.2sin²θ
  4. D.2sec²θ

Explanation

cosθ/(secθ−1) + cosθ/(secθ+1) = cosθ[(secθ+1+secθ−1)/((secθ)²−1)] = cosθ[2secθ/tan²θ] = cosθ×(2/cosθ)×(cos²θ/sin²θ) = 2cos²θ/sin²θ = 2cot²θ.
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