9) (14 points) Find the range of the function $f(x)=\sin ^{4} x \cdot \tan x+$ $\cos ^{4} x \cdot \cot x$.
(9) Since
$$
\begin{aligned}
f(x) & =\sin ^{4} x \cdot \frac{\sin x}{\cos x}+\cos ^{4} x \cdot \frac{\cos x}{\sin x} \\
& =\frac{\sin ^{6} x+\cos ^{6} x}{\sin x \cos x} \\
& =\frac{2-\frac{3}{2} \sin ^{2} 2 x}{\sin 2 x},
\end{aligned}
$$

Let $t=\sin 2 x$, then $t \in[-1,0) \cup(0,1]$,
$$
f(x)=\frac{2-\frac{3}{2} t^{2}}{t}=\frac{2}{t}-\frac{3}{2} t .
$$

It is easy to see that the function $g(t)=\frac{2}{t}-\frac{3}{2} t$ is decreasing on the intervals $[-1,0)$ and $(0,1]$, so the range of $g(t)$ is $\left(-\infty,-\frac{1}{2}\right] \cup\left[\frac{1}{2},+\infty\right)$, hence the range of $f(x)$ is $\left(-\infty,-\frac{1}{2}\right] \cup\left[\frac{1}{2},+\infty\right)$.