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Math Help - Prove the addition problem of cos.

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    Prove the addition problem of cos.

    How do you prove the addition formula for cos?
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  2. #2
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    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
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