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Math Help - Prove equation

  1. #1
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    Prove equation

    cosh2 theta= 2sinh^2 theta

    I did this = 2.(e^theta -e^-theta)/2 x(e^theta -e^-theta)/2
    =2 x 1/4(e^2theta + e^-2 theta)
    =(e^2theta +e^-2theta)/2
    = cosh2 theta
    I am trying to get the hang of this Latex
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  2. #2
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    Quote Originally Posted by Jaffa View Post
    cosh2 theta= 2sinh^2 theta

    I did this = 2.(e^theta -e^-theta)/2 x(e^theta -e^-theta)/2 (1)
    =2 x 1/4(e^2theta + e^-2 theta) (2)
    =(e^2theta +e^-2theta)/2
    = cosh2 theta
    I am trying to get the hang of this Latex
    Unfortunately, that's not the identity (and besides step (1) to (2) is wrong - there's a cross term missing). The identity is

    \cosh 2 x = \cosh^2 x + \sinh^2 x

    Proof:
     \cosh^2 x + \sinh^2 x = \left( \frac{e^x + e^{-x} }{2} \right) ^2 + \left( \frac{e^x - e^{-x} }{2} \right) ^2 = \frac{e^{2x} + 2 + e^{-2x}}{4} + \frac{e^{2x} - 2 + e^{-2x}}{4}
     = \frac{e^{2x} + e^{-2x}}{2} = \cosh 2x
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