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Question
Prove the following trigonometric identities.
sin2 A cos2 B − cos2 A sin2 B = sin2 A − sin2 B
Solution
We know that `sin^2 A + cos^2 A = 1`
So have
`sin^2 A cos^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 A sin^2 B`
`= sin^2 A - sin^2 B`
Hence proved.
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