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SSC CGL 2022 PYQ — Question 62

SSC CGL - 05 Dec 2022 - Shift 2 • Quantitative Aptitude • Q62

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Find the value of 1+cos⁡θ1−cos⁡θ+1−cos⁡θ1+cos⁡θ\sqrt \frac {1+ \cos \theta}{1-\cos\theta} + \sqrt \frac {1- \cos \theta}{1+\cos\theta}

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 2 cosec θ.

Concept Used:

sin2A = 1 - cos2A

1/sinA = cosecA

Explanation:

From the given question, rationalising both the terms, we get

(1+cosθ)(1+cosθ)(1−cosθ)(1+cosθ)+(1−cosθ)(1−cosθ)(1+cosθ)(1−cosθ)\sqrt{(1 +cos\theta)(1 + cos\theta) \over (1 - cos\theta)(1 + cos\theta)} + \sqrt{(1 - cos\theta)(1 - cos\theta) \over (1 + cos\theta)(1 - cos\theta)}

⇒ (1+cosθ)2(1−cos2θ)+(1−cosθ)2(1−cos2θ)\sqrt{(1+cos\theta)^2 \over (1 - cos^2\theta)} + \sqrt{(1 - cos\theta)^2 \over (1 - cos^2\theta)}

⇒ (1+cosθ)(sinθ)+(1−cosθ)(sinθ){(1 + cos\theta) \over (sin\theta)} + {(1 - cos\theta) \over (sin\theta)} 

⇒ cosecθ+cotθ+cosecθ−cotθcosec\theta + cot\theta + cosec\theta - cot\theta 

⇒ 2 cosec θ

Hence the value of 1+cos⁡θ1−cos⁡θ+1−cos⁡θ1+cos⁡θ\sqrt \frac {1+ \cos \theta}{1-\cos\theta} + \sqrt \frac {1- \cos \theta}{1+\cos\theta} is 2 cosec θ.