Results 1 to 3 of 3

Math Help - hyperbolics!

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    17

    hyperbolics!

    can someone offer advise with this one please?


    prove: cosh 2theta=2sinh^2 theta + 1

    can anyone advise how to resolve this one honestly dont know where to start with it.

    thankyou

    any pointers appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,315
    Thanks
    1225
    Quote Originally Posted by ads114 View Post
    can someone offer advise with this one please?


    prove: cosh 2theta=2sinh^2 theta + 1

    can anyone advise how to resolve this one honestly dont know where to start with it.

    thankyou

    any pointers appreciated.

    \cosh{2\theta} = \cosh^2{\theta} + \sinh^2{\theta}

     = 1 + \sinh^2{\theta} + \sinh^2{\theta}

     = 2\sinh^2{\theta} + 1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,306
    Thanks
    1282
    Or, directly from the definition, since sinh(\theta)= \frac{e^{\theta}- e^{-\theta}}{2},

    sinh^2(\theta)= \frac{e^{2\theta}- 2+ e^{-2\theta}}{4}= \frac{e^{2\theta}+ e^{-2\theta}}{4}- \frac{1}{2} so

    2sinh^2(\theta)= \frac{e^{2\theta}+ e^{-2\theta}}{2}-1 and then

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

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 19th 2010, 03:48 PM
  2. Hyperbolics
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 11th 2009, 02:34 PM
  3. hyperbolics
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: September 6th 2009, 04:02 AM
  4. Hyperbolics
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 19th 2008, 01:57 PM
  5. can't integrate powers of hyperbolics
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 9th 2007, 05:38 AM

Search Tags


/mathhelpforum @mathhelpforum