Question

sin^4x+cos^4x = cos4x

Answer 1

$sin ^4x+cos^4x=cos4x\ sin^4x+2cos^2xsin^2x+cos^4x-2cos^2xsin^2x=cos 4x\ (sin^2x+cos^2x)^2-0.5sin^22x=1-2sin^22x\ 1-0.5sin^22x=1-2sin^22x\ 1.5sin^22x=0\ sin2x=0\ 2x=pi k,k in mathbb{Z}\ \ boxed{x=frac{pi k}{2},k in mathbb{Z}}$