Mathematics
Find the magnitude of angle A, if :
2 sin A cos A - cos A - 2 sin A + 1 = 0
Trigonometric Identities
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Answer
2 sin A cos A - cos A - 2 sin A + 1 = 0
⇒ (2 sin A cos A - cos A) - (2 sin A - 1) = 0
⇒ cos A(2 sin A - 1) - 1(2 sin A - 1) = 0
⇒ (2 sin A - 1)(cos A - 1) = 0
⇒ (2 sin A - 1) = 0 or (cos A - 1) = 0
⇒ 2 sin A = 1 or cos A = 1
⇒ sin A = or cos A = 1
⇒ sin A = sin 30° or cos A = cos 0°
⇒ A = 30° or 0°
Hence, A = 30° or 0°.
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