What is 3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}+4(\sin x)^{6}+4(\cos x)^{6} equal to?

Explanation

Since the expression is an identity, it holds for all values of x. Put x=0. Then \sin 0 = 0 and \cos 0 = 1. The expression becomes 3(0-1)^4 + 6(0+1)^2 + 4(0)^6 + 4(1)^6 = 3(1) + 6(1) + 0 + 4 = 13.

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