Given:

$\displaystyle \alpha+\beta=\frac{\pi}{2}+\frac{x}{2}$

$\displaystyle \sin(\alpha)=y$

$\displaystyle \tan^2(\beta)=\frac{a}{\lambda y^2}\frac{a-\lambda y^2}{a-1}$

$\displaystyle a=\frac{1}{2}\left(1+\lambda + \sqrt{(1+\lambda)^2-4\lambda y^2}\right)$,

solve for y(x) where $\displaystyle \lambda$ is a known parameter.

I'm having a hard time doing this - please help!