Question

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

Answer 1

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

Отсюда:

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

или

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