# Hyperbolic Function Proof

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• November 9th 2008, 11:45 PM
U-God
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.
• November 10th 2008, 12:24 AM
flyingsquirrel
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.