Answer
It is NOT an identity.
Work Step by Step
Graphing $f(x)=(\sin x + \cos x)^2$ and $g(x)=1$ 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.
Two different graphs are present so this is NOT an identity.
