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प्रश्न
Prove the following identity :
`sin^2Acos^2B - cos^2Asin^2B = sin^2A - sin^2B`
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उत्तर
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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Activity:
L.H.S. = `square`
= (sin2A + cos2A) `(square)`
= `1 (square)` ...`[sin^2"A" + square = 1]`
= `square` – cos2A ...[sin2A = 1 – cos2A]
= `square`
= R.H.S.
