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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

enter image description here

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Note that $\sin 2x=2\sin x \cos x$. – Gigili Mar 1 '12 at 12:05

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.

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