This can be written:
(1+sin(x))/cos(x)=cos(x),
1+sin(x)=cos2(x)=1-sin2(x),
sin(x)=-sin2(x),
sin(x)(sin(x)+1)=0.
So sin(x)=0 or sin(x)=-1.
x=πn or x=3π/2+2πn where n is an integer. x is in radians.
In degrees this is: x=180n or 270+360n.
However, the original equation is undefined when x=270+360n so, strictly, the only solution is x=πn (180n degrees).