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Thread: Proving Euler's formula in two ways.

  1. #1
    Senior Member x3bnm's Avatar
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    Proving Euler's formula in two ways.

    I tried to prove Euler's formula using two different methods.

    I would appreciate if anyone would kindly check if I have made any mistakes with the proves.


    proofofeulersformula.pdf
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  2. #2
    MHF Contributor
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    Re: Proving Euler's formula in two ways.

    Hey x3bnm.

    Hint - Try considering matching up e^x [for taylor series] with what you got with your cosine and sine taylor series and show they match term for term.
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  3. #3
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    Re: Proving Euler's formula in two ways.

    Your second method starts with $\displaystyle e^{i\theta}= cos(\theta)+ i sin(\theta)$. convert to $\displaystyle 1= \frac{e^{i\theta}}{cos(\theta)+ i sin(\theta)}$ and show that the derivative of both sides is 0.

    That is not logically valid. First, you start by asserting what you want to show. That can be used in what is sometimes called "synthetic proof"- assert what you want to show then reduce to an obviously true statement- provided every step is "invertible". But the derivative is NOT invertible. The fact that f'(x)= g'(x) does NOT imply that f(x)= g(x).
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