cos(2x)+sin(x)=0,
1-2sin²(x)+sin(x)=0,
2sin²(x)-sin(x)-1=0,
(2sin(x)+1)(sin(x)-1)=0,
sin(x)=-½, x=-π/6 or -30º.
The more general answer is x=2πn-π/6, or 360n-30 degrees, where n is an integer. Also 7π/6+2πn (360n+210 degrees).
Also, sin(x)=1, so x=π/2 (90º) or, more generally, 2πn+π/2.