1. The smallest positive period of the function $f(x)=|\sin 2 x+\cos 2 x|$ is ( ).
(A) $2 \pi$
(B) $\pi$
(C) $\frac{\pi}{2}$
(D) $\frac{\pi}{4}$
- 1. C.

Notice,
$$
\begin{array}{l}
f(x)=|\sin 2 x+\cos 2 x| \\
\Leftrightarrow f(x)=\left|\sqrt{2} \sin \left(2 x+\frac{\pi}{4}\right)\right| .
\end{array}
$$

By the relationship between function graphs, it is known that $f(x)$ and $g(x)=|\sin 2 x|$ have the same smallest positive period.

Since the smallest positive period of $|\sin x|$ is $\pi$, therefore, the smallest positive period of $g(x)$ is $\frac{\pi}{2}$.