Plot f(x) vs g(y) for the system F(f(x), g(y), x, y) = 0 and G(x,y) = 0

Question

I have the following system of functions:

   F( f(x), g(y), x, y) = 0,

   G(x,y) = 0

My specific example is:

G =[sin(x) - cos(y)-