1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Hyperbolic cosine identity help!

  1. Jan 24, 2012 #1
    1. The problem statement, all variables and given/known data

    Show that cosh^2(x) = (cosh(2x) - 1)/2

    2. Relevant equations

    cosh(x) = (e^x + e^-x)/2

    3. The attempt at a solution

    I have attempted this multiple times and get the same results every time.
    Squaring cosh(x) I get 1/4(e^2x + e^-2x +2), which is i believe 1/4(cosh(2x) +2).

    Maybe i just can't see it but how it that equivalent to the identity above??
    Last edited: Jan 24, 2012
  2. jcsd
  3. Jan 24, 2012 #2


    User Avatar
    Homework Helper

    wait, so what are you trying to show?

    the first is just normal double angle cos and can be shown by looking at Re and Im of (e^(itheta))^2
    Last edited: Jan 24, 2012
  4. Jan 24, 2012 #3


    User Avatar
    Science Advisor
    Homework Helper

    welcome to pf!

    hi s.perkins! welcome to pf!:smile:
    erm :redface:

    cosh(x) = (e^x plus e^-x)/2 :wink:
  5. Jan 24, 2012 #4


    User Avatar
    Homework Helper

    looks like the correct form has been used in the square, but also don't forget the factor of 2 as well...
  6. Jan 24, 2012 #5
    Sorry fixed the typo. I did include the 1/2, when its squared you get a 1/4 in front.
  7. Jan 24, 2012 #6


    User Avatar
    Homework Helper

    might as well use equals as its a bit clearer what you're trying

    here should be

    = (e^2x + e^-2x +2)/4
    = (2(e^2x + e^-2x)/2 +2)/4
    = (2cosh(2x) +2)/4
    = (cosh(2x) +1)/2

    which is a valid identity, as shown by adding th two below together
    cosh(x)^2- sinh(x)^2=1
    which gives
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook