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SSC CPO 2024 PYQ — Question 131

SSC CPO - 27 June 2024 - Shift 2 • Quantitative Aptitude • Q131

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If sin α = 513\frac{5}{13} then the value of cosα . cosecα . cotα is

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Correct answer: C

Explanation

The correct answer is Option 3 i.e. 14425\frac{144}{25}.

sin α = 5/13

sin2 α + cos2 α = 1

⇒ cos2 α = 1 - (5/13)2 = 1 - 25/169 = 144/169 

⇒ cos α = √(144/169) = 12/13

⇒ cosec α = 1/(sin α) = 1/(5/13) = 13/5

⇒ cot α = (cos α)/(sin α) = (12/13)/(5/13) = 12/5

 cos α . cosec α . cot α = (12/13) × (13/5) × (12/5) = 144/25