Ok here is what I figured out so far. By pluging those 2 functions in to the equation and squaring it I getGiven that

$\displaystyle f(x) = \frac {e^x + e^{-x}}{2}$ and $\displaystyle g(x) = \frac {e^x - e^{-x}}{2}

$ show that $\displaystyle

[f(x)]^2 - [g(x)]^2 = 1$

$\displaystyle \frac {e^{2x} + e^{-2x}}{4} - \frac {e^{2x} + e^{-2x}}{4} = 1$.

Here's my question though. Wouldn't that make it equal $\displaystyle 0$ once you subtract all the variables, as it would be $\displaystyle \frac {0}{4}$, which is equal to $\displaystyle 0$.