If (2cosA + 1)(2cosA – 1) = 0, 0° < A ≤ 90°, then find the value of A.
Explanation:
(2cosA + 1)(2cosA – 1) = 0
⇒ 4cos2A - 1 = 0
⇒ 4cos2A – (cos2A + sin2A) = 0
⇒ 3cos2A – sin2A = 0
⇒ 3cos2A = sin2A
⇒ sin2Acos2A =3
⇒ tan2A = 3
⇒ tanA = √3
∴ A = 60°
Hence, option (c).
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