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Problem with hyperbolic functions demostrations!

  1. Dec 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that [itex]cosh (\frac{x}{2}) = \sqrt{\frac{cosh(x)+1}{2}}[/itex]


    2. Relevant equations
    [itex]cosh(x) = \frac{e^{x}+e^{-x}}{2}[/itex]



    3. The attempt at a solution
    [itex]\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}}}[/itex]

    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. jcsd
  3. Dec 27, 2012 #2
    [tex]
    cosh^2\frac{x}{2}=\frac{e^x+e^{-x}+2}{4}=\frac{cosh(x)+1}{2}
    [/tex]
    That's it!
     
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