Question

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`?

Answer 1

see below

Explanation:

Well, first you simplify this

`y = cos^2 x - sin ^2 x = cos 2x` 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 `color(red)(2x)`, ie a full cycle has period `pi` rather than `2 pi`

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