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Question
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
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Solution
L.H.S = sin(A + B) sin(A – B)
= (sin A cos B + cos A sin B) (sin A cos B – cos A sin B)
= sin2A cos2B – cos2A sin2B
= sin2A(1 – sin2B) – (1 – sin2A) sin2B
= sin2A – sin2A sin2B – sin2B + sin2A sin2B
= sin2A – sin2B
= R.H.S
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