Решить уравнение : sin2x/tgx-cosx=0

$frac{sin2x }{tgx} - cosx = 0$
$frac{2sinx * cosx}{ frac{sinx}{cosx} } - cosx = 0$
$frac{2sinx*cosx*cosx}{sinx} - cosx = 0$
$2cos^{2} x - cosx = 0$
$cosx(2cosx-1)=0$
$cosx = 0$ $2cosx-1=0$
$x = frac{ pi }{2} + pi n$ $2cosx=1$
$cosx= frac{1}{2}$
$x = -+arccos frac{1}{2} + 2 pi n$
$x = -+ frac{ pi }{3} +2 pi n$