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Homework Help: Hyperbolic Functions

  1. Apr 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Given the trigonometric identity cos(x+y)... use Osborn's rule to write down the corresponding identity for cosh(x+y)... Use the definitionis of the hyperbolic functions to prove this identity

    2. Relevant equations



    3. The attempt at a solution

    I can use Osborns rule to find the hyperbolic equivilent of the identity, however, I don't understand how I am to prove this identity...
     
  2. jcsd
  3. Apr 25, 2008 #2

    rock.freak667

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    Homework Helper

    [itex]cos(x+y)=cosxcosy-sinxsiny[/itex]

    Osborn said that when you have the product of two sines, you replace the sines with sinh and a negative sign.

    so therefore [itex]cosh(x+y)=cosxcosy-(-sinhxsinhy)[/itex]
     
  4. Apr 26, 2008 #3

    exk

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    rock.freak missed the h in his last bit for the 2 cos terms on the rhs.
    [itex]
    cosh(x+y)=coshxcoshy-(-sinhxsinhy)
    [/itex]
     
  5. Apr 26, 2008 #4

    HallsofIvy

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    Okay, you already know that cosh(x+ y)= cosh(x)cosh(y)+ sinh(x)sinh(y). Now replace cosh(x) by [itex](e^x+ e^{-x})/2[/itex], replace sinh(x)= [itex](e^x- e{-x})/2[/tex], the corresponding things for cosh(y) and sinh(y) and do the algebra. What do you get when you multiply
    [tex]\frac{e^x+ e^{-x}}{2}\frac{e^y+ e^{-y}}{2}[/tex]
     
    Last edited by a moderator: Apr 26, 2008
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