# Math Help - Hyperbolic Function Proof

1. ## Hyperbolic Function Proof

Hey guys, I've just been doing a few different proofs to do with hyperbolic functions and I'm stuck on this one:

$[cosh(x) + sinh(x)]^n = cosh(nx) + sinh(nx)$

I attempted to rewrite it in exponential form with no avail..

If someone could point me in the right direction to begin with it would be fantastic, thanks.

2. Hi,

Well the LHS is $\left(\frac{\mathrm{e}^x+\mathrm{e}^{-x}}{2} +\frac{\mathrm{e}^x-\mathrm{e}^{-x}}{2} \right)^n$ and the RHS is $\frac{\mathrm{e}^{nx}+\mathrm{e}^{-nx}}{2} +\frac{\mathrm{e}^{nx}-\mathrm{e}^{-nx}}{2}$. If you simplify these two expressions you'll see that they equal one another.