# How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for  y=cos^2 x - sin^2 x?

Aug 20, 2016

see below

#### Explanation:

Well, first you simplify this

$y = {\cos}^{2} x - {\sin}^{2} x = \cos 2 x$ is a well known identity ... a double angle formulae

then it's just a periodic cosine, save that it has twice the frequency as it is the cosine of $\textcolor{red}{2 x}$, ie a full cycle has period $\pi$ rather than $2 \pi$

graph{cos (2x) [-2.738, 2.736, -1.367, 1.37]}