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Math Help - Hyperbolic Function Proof

  1. #1
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    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.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    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.
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