Results 1 to 2 of 2

Math Help - Prove the addition problem of cos.

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    22

    Prove the addition problem of cos.

    How do you prove the addition formula for cos?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by Swamifez View Post
    How do you prove the addition formula for cos?
    Which level are you on?
    High school or college?
    ---
    If college.
    ---
    Then,
    exp (ix)=cos x+i*sin x
    exp (-ix)=cos x-i*sin x

    Add,
    exp(ix)+exp(-ix) =2cos x
    Thus,
    cos x=(exp(ix)+exp(-ix))/2=cosh (ix)

    Substract,
    exp(ix)-exp(ix)=2i*sin x
    Thus,
    sin x=(exp(ix)+exp(-ix))/2i=-i*sinh (ix)

    Thus when you want to show,
    cos(x+y)=cos x*sin y+sin x*cos y
    Just substitute those identities into the equation and show the left and right hands match
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. word addition problem
    Posted in the Algebra Forum
    Replies: 5
    Last Post: April 30th 2011, 07:03 PM
  2. Vector Addition Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 13th 2010, 05:27 AM
  3. Prove Addition Exists....Sorta
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 13th 2010, 10:10 PM
  4. Replies: 4
    Last Post: April 13th 2010, 07:09 PM
  5. Addition problem
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 19th 2009, 12:11 PM

Search Tags


/mathhelpforum @mathhelpforum