If cot A cosec A and A is an acute angle then the value of cos A is ........

Quantitative Aptitude ( CCS) Trignometry

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If cot A + cosec A = and A is an acute angle, then the value of cos A is

4/5

1/2

1/√3

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Explanation:

Here, cot A + cosec A = 3
⇒ cosA /sinA + 1/sinA = 3
⇒ cos A + 1 = 3sin A
Squaring both sides.
⇒ (cos A + 1)² = 9sin² A
⇒ cos² A + 2cos A + 1 = 9 (1 – cos² A)
⇒ 10 cos²A + 2 cos A – 8 = 0
⇒ 5 cos² A + cosA – 4 = 0
⇒ (5 cos A – 4)(cos A + 1) = 0
(? A is an acute angle)
∴ cos A = 4/5