Question

sin^2x/2 - cos^2x/2 = корень из 2/2

Answer 1

$sin^2 frac{x}{2}-cos^2 frac{x}{2}=frac{sqrt{2}}{2}$
$-cos (2*frac{x}{2})=frac{sqrt{2}}{2}$
$cos x=-frac{sqrt{2}}{2}$
$x=^+_-(pi-arccos frac{sqrt{2}}{2})+2*pi*k$
$x=^+_-(pi-frac{pi}{4})+2*pi*k$
$x=^+_-frac{3pi}{4}+2*pi*k$,
k є Z