sin(2x)=cos(x+30),
cos(90-2x)=cos(x+30),
90-2x=x+30,
60=3x, x=20° is one solution but there are many others.
sin(2x)=sin(360n+2x) where n is an integer.
So cos(90-360n-2x)=cos(x+30),
90-360n-2x=x+30,
90-30-360n=3x,
60-360n=3x,
x=20-120n. This can also be written x=20+120n since n is an arbitrary integer.
x= 20, 140, 260, 380, ... degrees.
Also, cos(-x-30)=cos(x+30), so:
90-360n-2x=-x-30,
120-360n=x which can be written x=120+360n,
x=120, 480, 840, ... degrees.