help on using maxima to solve systems of equations

Harald wrote:

>Maxima treats any symbol not mentioned as variable as arbitrary parameter.
>It finds out that [e1, e2] is not consistent for arbitrary values
>of b, c, x, y. Any of them is determined by the three others so just
>pick one as additional variable. For example:
>(%i10) solve([e1,e2],[a,c]);
>(%o10) [[a = (y-b)/x,c = (y-b)/x]]

Thanks, that helps!

I have another question (again a simplified example):

(%i1) e1:x2=x*cos(phi)-y*sin(phi);
(%o1) x2=cos(phi)*x-sin(phi)*y
(%i2) e2:y2=x*sin(phi)+y*cos(phi);
(%o2) y2=cos(phi)*y+sin(phi)*x
(%i3) solve([e1,e2],[x,y]);
(%o3) [[x=(sin(phi)*y2+cos(phi)*x2)/(sin(phi)^2+cos(phi)^2),y=-(sin(phi)*x2-cos(phi)*y2)/(sin(phi)^2+cos(phi)^2)]]

How can I get Maxima to recognize that sin(phi)^2+cos(phi)^2 = 1 ? Without this type of simplification, the solutions of my system will get huge and ugly. 

greetings,
Tom