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Math Help - prove the trig identity

  1. #1
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    prove the trig identity

    Hi, the question is: starting from the definition of the complex cosine function, prove the trig identity:
     cos^2z=\frac{1}{2}(1 + cos 2z)

    here's what i got
     cos^2 z = [\frac{1}{2}(e^{iz}+e^{-iz}]^2
     = \frac{1}{4}(e^{2iz}+e^{-2iz} + 2)
     = \frac{1}{2}(\frac{1}{2} (e^{2iz} + e^{-2iz} + 1)
    and now i don't know what to do.. is this right so far? and can someone please help me finish it off?
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  2. #2
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    Quote Originally Posted by Dgphru View Post
    Hi, the question is: starting from the definition of the complex cosine function, prove the trig identity:
     cos^2z=\frac{1}{2}(1 + cos 2z)

    here's what i got
     cos^2 z = [\frac{1}{2}(e^{iz}+e^{-iz}]^2
     = \frac{1}{4}(e^{2iz}+e^{-2iz} + 2)
     = \frac{1}{2}(\frac{1}{2} (e^{2iz} + e^{-2iz} + 1)
    and now i don't know what to do.. is this right so far? and can someone please help me finish it off?

    You alredy did everything!

    \frac{1}{4}\left(e^{2iz}+e^{-2iz} + 2\right) <br />
=\frac{1}{2}\left(\frac{e^{2iz}+e^{-2iz}}{2}+1\right)=\frac{1}{2}\left(\cos 2z+1\right) ...

    Tonio
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