1. The smallest positive period of the function $f(x)=\cos ^{4} x+\sin ^{2} x(x \in \mathbf{R})$ is ( ).
(A) $\frac{\pi}{4}$
(B) $\frac{\pi}{2}$
(C) $\pi$
(D) $2 \pi$
$$
\begin{array}{l}
f\left(x+\frac{\pi}{2}\right)=\sin ^{4} x+\cos ^{2} x \\
=\sin ^{4} x+\cos ^{4} x+\cos ^{2} x \cdot \sin ^{2} x \\
=\cos ^{4} x+\sin ^{2} x=f(x) . \\
\text { Also, } f(0)=1 \text{ and } f\left(\frac{\pi}{4}\right)=\frac{1}{4}+\frac{1}{2} \neq f(0), \text { therefore }
\end{array}
$$

Choose (B).