Prove $x^2+y^2=1$

[Guest]

Let $x=\frac{a(ac\sin^{2}\alpha+b^{2}\cos \alpha)}{a^{2}\sin^{2}\alpha+b^{2}\cos^{2}\alpha}$ and $y=,\frac{ab\sin \alpha(a-c\cos \alpha)}{a^{2}\sin^{2}\alpha+b^{2}\cos^{2}\alpha}$.

Prove: $x^2+y^2=1$

Could you please help me to prove this? I only get extremely long terms if I try to square $x$ and $y$. $sin^2+cos^2=1$ doesn't seem to help either.

[HallsofIvy]

What does
[tex]x= \begin{array}{cc} a(ac\sin^2(/alpha)+ b^2\cos(\alpha)) \\ a^2 \sin^2(\alpha)+ b^2\cos^2(\alpha)\end{array}[/tex]
mean? Is it a 2 dimensional vector? What ever it is, how is [tex]x^2[/tex] defined?
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