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Thread: Trigonometric equation

  1. #1
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    Trigonometric equation

    $$\sin{x}+\sin{2x}+\sin{3x}+\sin{4x}=0$$

    I'm having a lot of trouble solving this... Didn't really get anywhere so nothing to show. I assume the solution has something to do with the fact that
    4x + x = 5x, and 2x + 3x = 5x, but I have absolutely no idea
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  2. #2
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    Re: Trigonometric equation

    Nevermind I figured it out.
    $$\sin(2x-x)+\sin(2x+x)+\sin(3x-x)+\sin(3x+x)=0$$
    $$2\sin{2x}\cos{x}+2\sin{3x}\cos{x}=0$$
    $$\cos{x}(\sin{2x}+\sin{3x})=0$$

    And it's simple from there.

    Sorry.
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