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

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 $\sin 2x=2\sin x \cos x$. –  Gigili Mar 1 '12 at 12:05
If this was assigned as an Online Home Work, please add [homework] tag. –  user21436 Mar 1 '12 at 12:07

## 1 Answer

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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