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Mathematics

If (2 cos 2A - 1)(tan 3A - 1) = 0; find all possible values of A.

Trigonometric Identities

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Answer

Given,

⇒ (2 cos 2A - 1)(tan 3A - 1) = 0

⇒ 2 cos 2A - 1 = 0 or tan 3A - 1 = 0

⇒ 2 cos 2A = 1 or tan 3A = 1

⇒ cos 2A = 12\dfrac{1}{2} or tan 3A = tan 45°

⇒ cos 2A = cos 60° or tan 3A = tan 45°

⇒ 2A = 60° or 3A = 45°

⇒ A = 60°2\dfrac{60°}{2} or A = 45°3\dfrac{45°}{3}

⇒ A = 30° or 15°.

Hence, A = 30° or 15°.

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