# Math Help - Hyperbolic Trig Proof Help

1. ## Hyperbolic Trig Proof Help

Im stuck on the following problem and would greatly appreciate any help.

Using the exponential definitions of coshx and sinhx

$sinhx = (e^x - e^-x)/2$ and $coshx = (e^x + e^-x)/2
$

show that

$sinhx + sinhy = 2sinh((x+y) /2)cosh((x-y)/2)$

I know that it obviously involves use of the double angle formula but just cant get it work. Cheers

2. $2\sinh\frac{x+y}{2}\cosh\frac{x-y}{2}=\displaystyle 2\cdot\displaystyle\frac{e^{\frac{x+y}{2}}-e^{\frac{-x-y}{2}}}{2}\cdot\frac{e^{\frac{x-y}{2}}+e^{\frac{-x+y}{2}}}{2}=$

$=\frac{1}{2}\left(e^{\frac{x+y}{2}+\frac{x-y}{2}}+e^{\frac{x+y}{2}+\frac{-x+y}{2}}-e^{\frac{-x-y}{2}+\frac{x-y}{2}}-e^{\frac{-x+y}{2}+\frac{-x+y}{2}}\right)=$

$=\frac{1}{2}(e^x+e^y-e^{-y}-e^{-x})=\frac{e^x-e^{-x}}{2}+\frac{e^y-e^{-y}}{2}=\sinh x+\sinh y$

3. awesome thanks very much