# How do you find the period of y= 1 - 2(sin(2x))^2?

$y = 1 - 2 {\sin}^{2} \left(2 x\right)$
$y = 1 - 2 {\sin}^{2} \left(2 x\right) = \cos 4 x$
The period of y is $\frac{2 \pi}{4} = \frac{\pi}{2}$