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If A is an acute angle and cosec A + cot A = 3, then the value of cos A is?1). 2/52). 3/53). 4/54). 1/5 |
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Answer» ⇒ 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 |
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