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Math Help - Proof hyperbolic equation

  1. #1
    Junior Member freestar's Avatar
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    Proof hyperbolic equation

    Show that coth(x)+csc(x) = \frac{(1+e^-^1)^2}{1-(e^-^x)^2}.

    \frac{coshx}{sinhx}+\frac{1}{sinhx}

    \frac{e^x+e^-^x+2}{e^x-e^-^x}

    Can't understand how to approach from here.
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  2. #2
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    Re: Proof hyperbolic equation

    Hello, freestar!

    There is a typo in the first equation . . .


    . - - . . . . . . . . . . . . . . . . . . . . . . . . .
    Show that: . \coth(x)+\csch(x) \:=\: \frac{(1+e^{-1})^2}{1-(e^{-x})^2}.

    \frac{\cosh x}{\sinh x}+\frac{1}{\sinh x} \;=\;\frac{e^x+e^{-x}+2}{e^x-e^{-x}}

    Can't understand how to approach from here.

    We have: . \frac{e^x + 2 + e^{- x}}{e^x-e^{-x}}


    Divide numerator and denominator by e^x\!:

    . . \frac{1 + 2e^{-x} + e^{-2x}}{1-e^{-2x}} \;=\; \frac{(1-e^{-x})^2}{1 - (e^{-x})^2}

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