Simplifying an equation

**YoungMarbleGiant** · October 16th 2011, 04:58 PM

Can anyone shed light on how the following simplification was achieved?

I had: $4a^2 w^2 (coswt + cos2wt)^2 + 4a^2 w^2 (sin2wt - sinwt)^2$

Which became:

$8a^2 w^2 (1 + cos3wt)$

I expect there is a trig identity required but my mind is blank, help!

**SammyS** · October 16th 2011, 05:34 PM

To simplify things, look at $(\cos(2\theta) + \cos(\theta))^2 + (\sin(2\theta) - \sin(\theta))^2$

= $\cos^2(2\theta) +2\cos(2\theta)\cos(\theta) + \cos^2(\theta) + \sin^2(2\theta) -2\sin(2\theta)\sin(\theta) +\sin^2(\theta)$

$=2 + 2(\cos(2\theta)\cos(\theta)-\sin(2\theta)\sin(\theta))$

$=2 + 2\cos(2\theta+\theta)$

**YoungMarbleGiant** · October 16th 2011, 06:10 PM

Got it, thank you very much.

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