Question

$2sin^2x=sqrt{3}cos(frac{3pi}{2}+x)$

Answer 1

$cos(frac{3pi}{2}+x)=sinx$

$2sin^2x=sqrt{3}sin x\ sinx(2sinx-sqrt3)=0\ sinx=0\x=pi n\ sin x = frac{sqrt3}{2}\ x=(-1)^n frac{pi}{3}+pi n$