Answer
The graphs suggest that f(x)=g(x) is NOT an identity.
Work Step by Step
Graphing $f(x) = cos^{2}x$ - $sin^{2}x$ and $g(x) = 1-2sin^{2}x$ on the same rectangle in a graphing calculator we get the graph shown here. The blue graph is $f(x)$ and the red graph is $g(x)$. If this was an identity, then the graphs would overlap and look like just one graph. Thus, since we see two different graphs we know that $f(x)\ne g(x)$ and this is not an identity.
