E-ID04 · Two expressions with a fixed sum
Let \(P=(\sin x+\cos x)^2\) and \(Q=(\sin x-\cos x)^2\).
Prove that \(P+Q=2\) for all real \(x\).
If \(\displaystyle P=\frac32\), find \(Q\) and \(\sin x\cos x\).
Find every \(x\in[0,2\pi)\) for which \(P=Q\), without using a double-angle identity.
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