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SSC CGL 2022 PYQ — Question 61

SSC CGL - 12 April 2022 - Shift 2 • Quantitative Aptitude • Q61

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The value of 1 + cotθ+cosθcotθ−cosθ\sqrt{\frac{cot \theta + cos\theta}{cot \theta-cos \theta}}, if 0o < θ\theta < 90o, is equal to:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 1 + sec θ\theta + tan θ\theta.

1 + cotθ+cosθcotθ−cosθ\sqrt{\frac{cot \theta + cos\theta}{cot \theta-cos \theta}} =1+ cosθsinθ+cosθcosθsinθ−cosθ\sqrt{\frac{\frac{cos \theta}{sin \theta} + cos\theta}{\frac{cos \theta}{sin\theta} -cos \theta}}

= 1 + cosθ(1+sinθ)cosθ(1−sinθ)\sqrt{\frac{cos\theta(1+sin\theta)}{cos\theta(1-sin\theta)}}

= 1 + (1+sinθ)(1−sinθ)×(1+sinθ)(1+sinθ)\sqrt{\frac{(1+sin\theta)}{(1-sin\theta)}\times\frac{(1+sin\theta)}{(1+sin\theta)}}

= 1 +(1+sinθ)2(1−sin2θ)\sqrt{\frac{(1+sin\theta)^2}{(1-sin^2\theta)}}

= 1 +(1+sinθ)cosθ\frac{(1+sin\theta)}{cos\theta}

=  1 + sec θ\theta + tan θ\theta.