# Problem with hyperbolic functions demostrations!

1. Dec 27, 2012

### Rono

1. The problem statement, all variables and given/known data
Prove that $cosh (\frac{x}{2}) = \sqrt{\frac{cosh(x)+1}{2}}$

2. Relevant equations
$cosh(x) = \frac{e^{x}+e^{-x}}{2}$

3. The attempt at a solution
$\frac{\sqrt{e^{x}}+\sqrt{e^{-x}}}{2} \ast \frac{\sqrt{e^{x}}-\sqrt{e^{-x}}}{\sqrt{e^{x}}-\sqrt{e^{-x}}} \rightarrow \frac{e^{x}+e^{-x}}{2} \ast \frac{1}{\sqrt{e^{x}}-\sqrt{e^{-x}}} \rightarrow cosh(x) \ast \frac{1}{\sqrt{e^{x}}-\sqrt{e^{-x}}}$

After that, I don't know what to do. Would be glad if somebody would tell me what I'm doing wrong or how to do it. Thanks.

2. Dec 27, 2012

### kevinferreira

$$cosh^2\frac{x}{2}=\frac{e^x+e^{-x}+2}{4}=\frac{cosh(x)+1}{2}$$
That's it!

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