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SSC Selection Post 2024 PYQ — Question 54

SSC Selection Post - Higher Secondary Level - 26 June 2024 - Shift 2 • Quantitative Aptitude • Q54

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If A  is an acute angle, what is the value of cosec A, if cot A =2pp2−1?{{2p} \over p^2-1}?

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. p2+1p2−1{{p^2+1} \over p^2-1} .

cot A =2pp2−1{{2p} \over p^2-1}

⇒ 1+(2pp2−1)2=cosec2A1 + \left( \frac{2p}{p^2 - 1} \right)^2 = cosec^2 A

⇒ cosec2A=(p2−1)2+4p2(p2−1)2=(p2+1)2(p2−1)2cosec^2 A = \frac{(p^2 - 1)^2 + 4p^2}{(p^2 - 1)^2}= \frac{(p^2 + 1)^2}{(p^2 - 1)^2}

⇒ cosec A =p2+1p2−1={{p^2+1} \over p^2-1}