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Math Help - Simplification of hyperbolic function

  1. #1
    Ant
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    Simplification of hyperbolic function

    I'm having trouble seeing how this piece of manipulation follows:

    I can see that a factor of a 1/2 has been taken out but otherwise I'm unsure how to deal with the sinh(2arcsinh(wr))



    Any help would be appreciated!
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  2. #2
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    It's because \displaystyle \sinh{2x} = 2\sinh{x}\cosh{x}. In this case, \displaystyle x = \arcsin{(\omega \tau)}.


    BTW, are you sure that it's \displaystyle \sinh{[2\arcsin{(\omega \tau)}]} and not \displaystyle \sinh{[2\,\textrm{arcsinh}\,{(\omega \tau)}]}?
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  3. #3
    Ant
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    I hadn't even noticed it said sin. I'm pretty much certain that's a typo and as you say, it's supposed to be arcsinh.

    Thanks!
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