1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Homework Helper


    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


    User Avatar

    rock.freak missed the h in his last bit for the 2 cos terms on the rhs.
  5. Apr 26, 2008 #4


    User Avatar
    Staff Emeritus
    Science Advisor

    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: Apr 26, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Hyperbolic Functions
  1. Hyperbolic functions (Replies: 3)

  2. Hyperbolic functions (Replies: 2)

  3. Hyperbolic Functions (Replies: 1)

  4. Hyperbolic functions (Replies: 4)

  5. Hyperbolic Functions (Replies: 1)