SarkariPYQ

SSC Selection Post 2022 PYQ — Question 71

SSC Selection Post - Graduation Level - 9 Feb 2022 - Shift 3 • Quantitative Aptitude • Q71

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The value of tan2(22o−θ)−tan(θ+68o)−cosec2(68o+θ)+cot(22o−θ)3(cot252o−sec238o)+2(cosec228o−tan262o)tan^2(22^o-θ)-tan(θ+68^o)-cosec^2(68^o+θ)+cot(22^o-θ)\over3(cot^252^o-sec^238^o)+2(cosec^228^o-tan^262^o) is:

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 1.

tan2(22o−θ)−tan(θ+68o)−cosec2(68o+θ)+cot(22o−θ)3(cot252o−sec238o)+2(cosec228o−tan262o)tan^2(22^o-θ)-tan(θ+68^o)-cosec^2(68^o+θ)+cot(22^o-θ)\over3(cot^252^o-sec^238^o)+2(cosec^228^o-tan^262^o)

=cot2(68o+θ)−tan(68o+θ)−[1+cot2(68°+θ)]+tan(68°+θ)3(cot252°−cosec252°)+2(sec262°−tan262°)={cot^2(68^o+θ)-tan(68^o+θ)-[1 + cot^2(68° + θ)] + tan(68° + θ)\over3(cot^252° - cosec^252°)+2(sec^262° - tan^262°)}

=cot2(68o+θ)−1−cot2(68°+θ)3(−1)+2(1)={cot^2(68^o+θ)-1 - cot^2(68° + θ)\over3(-1)+2(1)}

= (- 1)/(- 3 + 2)

= (- 1)/(- 1)

= 1