Question

sin^2 x/2-cos^2 x/2=cos2x

Answer 1

$sin^2 frac{x}{2}-cos^2 frac{x}{2}=cos (2x)$
$-(cos^2 frac{x}{2}-sin^2 frac{x}{2})=cos (2x)$
$-cos (2*frac{x}{2})=2cos^2 x-1$
$-cos x=2cos^2 x-1$
$2cos^2 x+cos x-1=0$
$(2cos x-1)(cos x+1)=0$
$2cos x-1=0;cos x=frac{1}{2};x=^+_-frac{pi}{3}+2*pi*n$
n є Z
$cos x+1=0;cos x=-1;x=pi+2*pi*k$
k є Z