Answer
It is an identity
Work Step by Step
Graphing $f(x)=\cos^4 x - \sin^4 x$ and $g(x)= 2 \cos^2 x - 1$ on the same rectangle in a graphing calculator.
See graph below.
The red graph is f(x) and the black graph is g(x).
The graphs would overlap and look like just one graph if it was an identity.
One graph is present so this is an identity.
