<s>[INST] Remembering that $\sin^2(\theta) = 1/2 - 1/2\cos(2\theta)$? How do you remember this for integrals?
It doesn't seem obvious and I can never remember it when I come across it in integrals.
 [/INST] $\cos^2 \theta + \sin^2 \theta = 1$
$\cos^2 \theta - \sin^2 \theta = \cos 2\theta$  
Add and you get
$2\cos^2 \theta = 1 + \cos 2\theta$
$\cos^2 \theta = \frac 1 2 + \frac 1 2\cos 2\theta$
Subtract and you get
$2\sin^2 \theta = 1 - \cos 2\theta$
$\sin^2 \theta = \frac 1 2 - \frac 1 2\cos 2\theta$
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