1. ## Trig identity?

I'm having trouble trying to figure out how:

$\displaystyle \cos^22\theta$

turns into:

$\displaystyle 1/2 (1 + cos4\theta)$

Are we using some kind of trig identity?

Thanks!

2. Yes:

cos^2(t)=1/2{1+cos(2t)}

3. How do we get the cos4(t)?

4. Not sure what you're asking. The identity Also sprach Zarathustra mentioned is the power reduction identity.
$\displaystyle \cos^2 \,x = \dfrac{1}{2}(1 + \cos \,2x)$

Since you're looking for $\displaystyle \cos^2\,2\theta$, just plug in $\displaystyle 2\theta$ for $\displaystyle x$.