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SSC CGL 2022 PYQ — Question 77

SSC CGL Tier II - Quant - 3 Feb 2022 • Quantitative Aptitude • Q77

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If secθ−tanθsecθ+tanθ=17,θ\frac{sec \theta - tan \theta}{sec \theta + tan \theta}=\frac{1}{7}, \theta lies in the first quadrant, then the value of cosecθ+cot2θcosecθ−cot2θ\frac{cosec \theta + cot^2 \theta}{cosec \theta - cot^2 \theta} is:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 195\frac{19}{5}.

secθ−tanθsecθ+tanθ=17\frac{sec \theta - tan \theta}{sec \theta + tan \theta}=\frac{1}{7},

By using componendo and dividend we get,

(Secθ\theta - tanθ\theta + secθ\theta + tanθ\theta)/( Secθ\theta - tanθ\theta -  Secθ\theta - tanθ\theta ) = 8/-6

-Cosecθ\theta = -4/3

Cosecθ\theta = 4/3 = H/P

B = 16−9=7\sqrt{16 - 9} = \sqrt7.

cosecθ+cot2θcosecθ−cot2θ\frac{cosec \theta + cot^2 \theta}{cosec \theta - cot^2 \theta} = (4/3 + 7/9)/(4/3 - 7/9) = 19/5.