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    https://onedrive.live.com/redir?resi...nt=photo%2cJPG

    I don't get how you get from the second last line to the last line.

    Can someone explain?
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    It's all about cancellation

    Remember that

    \dfrac{a}{b} \times \dfrac{b}{c} = \dfrac{a}{c}
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    Not a fan of geometric proofs. Prefer using the fact that  \displaystyle \frac{1}{2}(e^{ix}-e^{-ix})=\sin x
    and  \displaystyle  \frac{1}{2}(e^{ix}+e^{-ix})=\cos x
    and then do it algebraically.
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    (Original post by B_9710)
    Not a fan of geometric proofs. Prefer using the fact that  \displaystyle \frac{1}{2}(e^{ix}-e^{-ix})=\sin x
    and  \displaystyle  \frac{1}{2}(e^{ix}+e^{-ix})=\cos x
    and then do it algebraically.
    But then your point is invalid because those equations rely on the compound angle formula.
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    (Original post by MathsAndChess)
    But then your point is invalid because those equations rely on the compound angle formula.
    No they don't.
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    (Original post by B_9710)
    No they don't.
    How do you prove that statement then?
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    (Original post by MathsAndChess)
    How do you prove that statement then?
    Complex numbers.
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    (Original post by B_9710)
    Complex numbers.
    I'm amusing you mean though the fact \exp(i\theta) = \cos \theta + i\sin \theta
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    (Original post by MathsAndChess)
    I'm amusing you mean though the fact \exp(i\theta) = \cos \theta + i\sin \theta
    Depends how you define sin and cos.
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    I guess if you're speaking from a geometric definition of sin and cos. Which I am then my statement is true. Else then I see why you wouldn't require this.
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    (Original post by MathsAndChess)
    I guess if you're speaking from a geometric definition of sin and cos. Which I am then my statement is true. Else then I see why you wouldn't require this.
    If you use the definitions above and find  \sin x \cos y +\cos x \sin y you will find that by the definition above that this is the same as  \sin(x+y) .
    You can find other results similarly.
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    (Original post by MathsAndChess)
    I guess if you're speaking from a geometric definition of sin and cos. Which I am then my statement is true. Else then I see why you wouldn't require this.
    Yeah if you use the geometric definitions you need to derive the double angle formulae before you can do anything interesting.
 
 
 
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