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Question
Prove the following identity :
`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`
Solution
LHS = `(cosA + sinA)^2 + (cosA - sinA)^2`
= `cos^2A + sin^2A + 2cosA.sinA + cos^2A + sin^2A - 2cosA.sinA`
= `2(cos^2A + sin^2A) = 2` = RHS
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