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Prove that sin (A + B) sin (A – B) = cos2 B – cos2 A |
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Answer» LHS = sin (A + B) sin (A – B) = (sin A cos B + cos A sin B) (sin A cos B – cos A sin B) = sin2 A cos2 B – cos2 A sin2 B = (1 – cos2 A) cos2 B – cos2 A (1 – cos2 B) = cos2 B – cos2 A cos2 B – cos2 A + cos2 A cos2 B = cos2 B – cos2 A = RHS |
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