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SSC CGL 2022 PYQ — Question 88

SSC CGL Tier II - Quant - 3 Feb 2022 • Quantitative Aptitude • Q88

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The value of 3(cosec2260−tan2640)+(cot2420−sec2480)cot(220−θ)−cosec2(620+θ)−tan(θ+680)+tan2(280−θ)\frac{3(cosec^226^0-tan^264^0)+(cot^242^0-sec^248^0)}{cot(22^0-\theta )-cosec^2(62^0+\theta )-tan(\theta+68^0 ) +tan^2(28^0-\theta )} is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. -2

We know that,

cosec2θ\theta - cot2θ\theta  = 1.

= 3(cosec2260−tan2640)+(cot2420−sec2480)cot(220−θ)−cosec2(620+θ)−tan(θ+680)+tan2(280−θ)\frac{3(cosec^226^0-tan^264^0)+(cot^242^0-sec^248^0)}{cot(22^0-\theta )-cosec^2(62^0+\theta )-tan(\theta+68^0 ) +tan^2(28^0-\theta )}

= 3(cosec2260−cot2(90−260)+(cot2420−cosec2(90−420)tan(90−220+θ)−cosec2(620+θ)−tan(θ+680)+cot2(90−280+θ)\frac{3(cosec^226^0-cot^2(90 - 26^0)+(cot^242^0-cosec^2(90 - 42^0)}{tan(90 - 22^0+\theta )-cosec^2(62^0+\theta )-tan(\theta+68^0 ) +cot^2(90 - 28^0+\theta )}

= (3 - 1)/(0 - 1) = -2.