The mapping T:R^2 -> R^2 is (x,y)=T(u,v)=(sinu/cosv, sinv/cosu).
I was able to prove that the mapping was 1 to 1 by setting T(u,v)=T(u',v') and showing that u=u' and v=v'.
I'm not sure how to show its onto. I think since I have x and y in terms of u and v, if i write u and v in terms of x and y, this will prove onto. The only problem is I am having trouble doing this.
I was given the hint to square both x(u,v) and y(u,v) and use sinx^2 +cosx^2=1 but i cant see how this helps.