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If A is an acute angle and cosec A + cot A = 3, then the value of cos A is?
- A2/5
- B3/5
- C4/5
- D1/5
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CCommunity
⇒ 1/sin A + cosA/sinA = 3
⇒ cosA + 1 = 3sin A
⇒ On squaring both sides, we get:-
⇒ cos2A + 2 cosA + 1 = 9 sin2A = 9(1 – cos2A)
⇒ 10cos2A + 2cosA – 8 = 0
⇒ 5cos2A + cosA – 4 = 0
⇒ 5cosA (cosA + 1) – 4 (cosA + 1) = 0
⇒ (cosA + 1) (5cosA – 4) = 0
Since A is an acute angle, ∴ cos A = 4/5
⇒ cosA + 1 = 3sin A
⇒ On squaring both sides, we get:-
⇒ cos2A + 2 cosA + 1 = 9 sin2A = 9(1 – cos2A)
⇒ 10cos2A + 2cosA – 8 = 0
⇒ 5cos2A + cosA – 4 = 0
⇒ 5cosA (cosA + 1) – 4 (cosA + 1) = 0
⇒ (cosA + 1) (5cosA – 4) = 0
Since A is an acute angle, ∴ cos A = 4/5