We have to prove that (sin x)^4 + (cos x)^4 + (sin 2x)^2/2 = 1
(sin x)^4 + (cos x)^4 + (sin 2x)^2/2
=> (sin x)^4 + (cos x)^4 + (2*sin x * cos x)^2/2
=> (sin x)^4 + (cos x)^4 + 4*(sin x)^2*(cos x)^2/2
=> (sin x)^4 + (cos x)^4 + 2*(sin x)^2*(cos x)^2
=> [(sin x)^2 + (cos x)^2]^2
=> 1^2
=> 1
This proves that (sin x)^4 + (cos x)^4 + (sin 2x)^2/2 = 1
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