Question

sin^4 x + cos^4 x=sin 2x

Answer 1

$sin^4 x+cos^4 x=sin (2x)$
$(sin^2 x+cos^2 x)^2-2sin xcos x-sin(2x)=0$
$1^2-sin(2x)-sin(2x)=0$
$1-2sin(2x)=0$
$sin(2x)=frac{1}{2}$
$2x=(-1)^k*frac{pi}{6}+pi*k$
k є Z
$x=(-1)^k*frac{pi}{12}+frac{pi*k}{2}$
k є Z