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Here's my problem, can someone show me the steps on doing this:

$\cos 5x − \cos 3x = −8 \sin^2 x(2 \cos^3 x − \cos x)$

Here is a link to my problem, I don't know what to put into the blanks though

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    Note that $\sin 2x=2\sin x \cos x$.2012-03-01

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Hint:

  • "Double angle identities":

    $\sin 2x = 2\sin x \cos x$ $\sin 4x = 2\sin 2x \cos 2x$ $\sin 8x = 2\sin 4x \cos 4x$ $\dots$

  • And the final blank is a simple multiplication.