10. (2004 National College Entrance Examination, National Volume) The minimum positive period of the function $f(x)=\frac{\sin ^{1} x+\cos ^{1} x+\sin ^{2} x \cos ^{2} x}{2-\sin 2 x}$ is $\qquad$ .
10.
$$
\begin{aligned}
f(x) & =\frac{\sin ^{1} x+\cos ^{1} x+\sin ^{2} x \cos ^{2} x}{2-\sin 2 x}=\frac{\left(\sin ^{2} x+\cos ^{2} x\right)^{2}-\sin ^{2} x \cos ^{2} x}{2(1-\sin x \cos x)} \\
& =\frac{1}{2}(1+\sin x \cos x)=\frac{1}{2}+\frac{1}{4} \sin 2 x
\end{aligned}
$$

The function $f(x)$ has the smallest positive period of $\pi$.