Question

sin2 A cos2 B-cos2 A sin2 B = sin2 A - sin2 B

Answer 1

$LHS = sin^{2} Acos^{2}B- cos^{2} A sin^{2} B \\= sin^{2} A ( 1 - sin^{2} B ) - ( 1 - sin^{2}A )sin^{2} B \\= sin^{2}A - sin^{2}A sin^{2} B - sin^{2}B + sin^{2}Asin^{2} B \\= sin^{2} A - sin^{2} B \\= RHS$

Therefore.,

$\red {sin^{2} Acos^{2}B- cos^{2} A sin^{2} B}$

$\green { = sin^{2} A - sin^{2} B}$

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