Cos²(x/2)-sin²(x/2)=sin(π/2-2x)

$cos^2 \frac{x}{2} -sin^2 \frac{x}{2} =sin( \frac{ \pi }{2} -2x)$
$cosx =cos2x$
$cosx -cos2x=0$
$-2sin \frac{x+2x}{2} *sin \frac{x-2x}{2} =0$
$-2sin 1.5x *sin(-0.5x)=0$
$2sin 1.5x *sin0.5x=0$
$sin 1.5x *sin0.5x=0$
$sin 1.5x=0$ или    $sin0.5x=0$
$1.5x= \pi k,$ $k$ ∈ $Z$    или    $0.5x= \pi n,$ $n$ ∈ $Z$
$x= \frac{2 \pi k}{3},$ $k$ ∈ $Z$ или    $x=2 \pi n,$ $n$ ∈ $Z$

$cos^2x-sin^2x=cos2x$
$sin( \frac{ \pi }{2} - \alpha )=cos \alpha$