Option 1 : 12/13

Given,

cotA + cosecA = 5 ----- (1)

We know that,

cosec^{2}x – cot^{2}x = 1

⇒ (cosec A + cot A)(cosec A – cot A) = 1 [∵ a2 – b2 = (a + b)(a – b)]

⇒ cosec A – cot A = 1/5 ----- (2)

Solving (1) & (2)

We get,

cosec A = 13/5 & cot A = 12/5

⇒ sin A = 5/13 (∵ cosec x = 1/sin x)

We know, cot A = cos A/sin A

⇒ cos A = cotA × sinA = (12/5) × (5/13) = 12/13

∴ cos A = 12/13SSC CHSL: Full Mock Test

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