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SSC CGL 2023 PYQ — Question 72

SSC CGL - 25 July 2023 - Shift 3 • Quantitative Aptitude • Q72

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The value of 1+cosθ1−cosθ\sqrt\frac{1+cos\theta}{1-cos\theta} is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. cosecθ+cot⁡θcosec\theta+\cot\theta.

  1+cosθ1−cosθ\sqrt\frac{1+cos\theta}{1-cos\theta} = 1+cosθ1−cosθ×1+cosθ1+cosθ\sqrt\frac{1+cos\theta}{1-cos\theta}×\sqrt\frac{1+cos\theta}{1+cos\theta}                 [muliplying by its conjugatory]

⇒ (1+cosθ)2(sinθ)2\sqrt\frac{(1+cos\theta)^2}{(sin\theta)^2} 

⇒ 1+cosθsinθ\frac{1+cos\theta}{sin\theta} = cosecθ+cot⁡θcosec\theta+\cot\theta