Question

Prove that: $4({\sin }^{4}x+{\cos }^{4}x)=\cos 4x+3$

Answer 1

$4({\sin }^{4}x+{\cos }^{4}x)$

$=4{({\sin }^{2}x+{\cos }^{2}x)}^2-2{\sin }^{2}x{\cos }^{2}x$

$=4-{\sin }^{2}2x$

$=3+1-{\sin }^{2}2x$

$=3+\cos 4x$