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Math Help - Solving a trigonometric equation

  1. #1
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    Solving a trigonometric equation

    sin a + sin 3a = cos a + cos 3a
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  2. #2
    MHF Contributor red_dog's Avatar
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    Use \sin a+\sin b=2\sin\frac{a+b}{2}\cos\frac{a-b}{2} and \cos a+\cos b=2\cos\frac{a+b}{2}\cos\frac{a-b}{2}

    Then,

    2\sin 2a\cos a=2\cos 2a\cos a

    2\cos a(\sin 2a-\cos 2a)=0

    Now you have to solve the equations:

    \cos a=0 and \sin 2a-\cos 2a=0\Leftrightarrow \tan 2a=1

    Can you do that?
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