Question

Sin^2x/2 - cos^2x/2 = корень из 2/2

Answer 1

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