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Question
Prove the following identity :
`cos^4A - sin^4A = 2cos^2A - 1`
Solution
LHS = `cos^4A - sin^4A`
= `(cos^2A - sin^2A)(cos^2A + sin^2A)`
= `{cos^2A - (1 - cos^2A)} = 2cos^2A - 1` = RHS
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