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4.42 Expressing trig powers in terms of multiple angles

In integration, it is easier to handle multiple angles than powers.

4.42.1 Example

To prove that

2\cos^{2}\theta=\cos 2\theta+1.

To prove that

\cos^{6}\theta={{1}\over{32}}\Bigl(\cos 6\theta+6\cos 4\theta+15\cos 2\theta+1% 0\Bigr).

This formula is useful for integrating $\cos^{6}\theta$ .