Results 1 to 3 of 3

Thread: Hyperbolic Trig Proof Help

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    23

    Hyperbolic Trig Proof Help

    Im stuck on the following problem and would greatly appreciate any help.

    Using the exponential definitions of coshx and sinhx


    sinhx = (e^x - e^-x)/2 and coshx = (e^x + e^-x)/2<br />

    show that

    sinhx + sinhy = 2sinh((x+y) /2)cosh((x-y)/2)

    I know that it obviously involves use of the double angle formula but just cant get it work. Cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    2\sinh\frac{x+y}{2}\cosh\frac{x-y}{2}=\displaystyle 2\cdot\displaystyle\frac{e^{\frac{x+y}{2}}-e^{\frac{-x-y}{2}}}{2}\cdot\frac{e^{\frac{x-y}{2}}+e^{\frac{-x+y}{2}}}{2}=

    =\frac{1}{2}\left(e^{\frac{x+y}{2}+\frac{x-y}{2}}+e^{\frac{x+y}{2}+\frac{-x+y}{2}}-e^{\frac{-x-y}{2}+\frac{x-y}{2}}-e^{\frac{-x+y}{2}+\frac{-x+y}{2}}\right)=

    =\frac{1}{2}(e^x+e^y-e^{-y}-e^{-x})=\frac{e^x-e^{-x}}{2}+\frac{e^y-e^{-y}}{2}=\sinh x+\sinh y
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2009
    Posts
    23
    awesome thanks very much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Hyperbolic trig identities?
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Aug 3rd 2011, 05:06 AM
  2. Hyperbolic Trig
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Feb 23rd 2010, 10:38 AM
  3. Hyperbolic Trig Proof
    Posted in the Calculus Forum
    Replies: 14
    Last Post: Mar 5th 2009, 09:18 PM
  4. proving a hyperbolic trig identity
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Jan 23rd 2008, 03:28 PM
  5. Need Calculus Help - Hyperbolic Trig Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 27th 2007, 10:11 PM

Search Tags


/mathhelpforum @mathhelpforum