If $5^x = \cos y$ and $a^x = \sin y$, then what is $\cos(2y)$ equal to?
I have tried squaring the first equation and then replacing the $\cos^2(x)$ with $1 - \sin^2 x$, and substituting into the second equation, but that has led me nowhere. Any other ideas?
Hint: Once you square $\cos y$ and $\sin y$ use the identity
$$\cos 2y = \cos^2 y - \sin^2 y$$