# What is cos^2theta in terms of non-exponential trigonometric functions?

$\frac{1 + \cos 2 x}{2}$
You use the duplication formula of $\cos$ :
$\cos 2 x = 2 {\cos}^{2} x - 1 \implies {\cos}^{2} x = \frac{1 + \cos 2 x}{2}$