Question

$2sin(\pi /2-x)*cos(3\pi /2+x)=\sqrt{3} sin(\pi -x)$

Answer 1

$2sin(\frac{\pi }{2}-x )*cos(\frac{3\pi}{2}+x)=\sqrt{3}sin(\pi -x) \\2sin(x)*cos(x)=\sqrt{3}sin(x)\\ 2sin(x)cos(x)-\sqrt{3}sin(x)=0\\ sin(x)*(2cos(x)-\sqrt{3} )=0$

Отсюда:

$sin(x)=0\\x=\pi*k$

или

$cos(x)=\frac{\sqrt{3} }{2}\\ x=(+-)\frac{\pi}{6}+2\pi *k$