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Math Help - find x

  1. #1
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    find x

    x is acute angle and

    \sin 5x \sin 4x=\sin 3x \sin 8x

    find x
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  2. #2
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    Quote Originally Posted by perash View Post
    x is acute angle and

    \sin 5x \sin 4x=\sin 3x \sin 8x

    find x
    Well, it's clear how some of the solutions can be got:

    \sin 5x \sin 4x=\sin 3x \sin 8x \, \Rightarrow \, \sin 5x \sin 4x= 2 \sin 3x \sin 4x \cos 4x.

    Therefore either:

    \sin 4x = 0 \, or \, \sin 5x = 2 \sin 3x \cos 4x.

    The first of these equations gives x = 0, \, \frac{\pi}{4} as (obvious) solutions. So there are only three other solutions to get .....
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