SarkariPYQ

SSC Selection Post 2024 PYQ — Question 55

SSC Selection Post - Higher Secondary Level - 26 June 2024 - Shift 2 • Quantitative Aptitude • Q55

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The value of cosecθ[1+cosθsinθ​cosec\theta[{{1+cos\theta} \over sin\theta} ​+sinθ1+cosθ]−2cot2θ+{{sin\theta} \over 1+cos\theta} ]-2cot^2\theta is equal to :

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Correct answer: C

Explanation

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

cosecθ[1+cosθsinθ​cosec\theta[{{1+cos\theta} \over sin\theta} ​+sinθ1+cosθ]−2cot2θ+{{sin\theta} \over 1+cos\theta} ]-2cot^2\theta

=cosec θ[(1+cos⁡θ)2+sin⁡2θsin⁡θ(1+cos⁡θ)]−2cot2 θ= cosec\,\theta[\frac{(1+\cos\theta)^2 + \sin^2\theta}{\sin\theta(1+\cos\theta)}]-2cot^2\,\theta

=cosec θ[2(1+cos⁡θ)sin⁡θ(1+cos⁡θ)]−2cot2 θ= cosec\,\theta[\frac{2(1+\cos\theta)}{\sin\theta(1+\cos\theta)}]-2cot^2\,\theta

= cosecθ (2/sinθ) - 2cot2θ

= 2/sin2θ - 2cot2θ

= 2cosec2θ - 2cot2θ

= 2