<s>[INST] Solve $3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}+4(\sin^{6} x+\cos^{6} x)$ Solve $3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}+4(\sin^{6} x+\cos^{6} x)$
$a.)\ 1 \\
\color{green}{b.)\ 13} \\
c.)\ 15 \\
d.)\ 16 $
$ 3(\sin x-\cos x)^{4}+6(\sin x+\cos x)^{2}+4(\sin^{6} x+\cos^{6} x)\\
=3(1-\sin (2x))^{2}+6(1+\sin 2x)+4(\sin^{6} x+\cos^{6} x)\\
=3(1-2\sin (2x)+\sin^{2} (2x))+6(1+\sin 2x)+4(\sin^{6} x+\cos^{6} x)\\
=9+3\sin^{2} 2x+4(\sin^{6} x+\cos^{6} x)\\
=9+12\sin^{2}x\times \cos^{2}x+4(\sin^{6} x+\cos^{6} x)\\$
I am stucked.
I look for a short and simple way.
I have studied maths upto $12$th grade.
 [/INST] The answer should be the same for all $x$. So plug in $x = 0$, 
$$3(-1)^4+6(1)^2+4(1)^6 = 13$$
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