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Question
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
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Solution
LHS = `sin^2A(1 - sin^2B) - (1 - sin^2A)sin^2B`
= `sin^2A - sin^2A.sin^2B - sin^2B + sin^2A.sin^2B`
= `sin^2A - sin^2B` = RHS
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