$9 \cdot 21$ Let $\alpha \neq \frac{1}{2} k \pi \quad(k=0, \pm 1, \pm 2, \cdots)$, and

then the possible values of $T$ are
$$
T=\frac{\sin \alpha+\operatorname{tg} \alpha}{\cos \alpha+\operatorname{ctg} \alpha},
$$
(A) $T$ takes negative values.
(C) $T$ takes positive values.
(B) $T$ takes non-negative values.
(D) $T$ can take both positive and negative values.
(China High School Mathematics League, 1981)
[Solution] By making an identity transformation, we easily get $T=\operatorname{tg}^{2} \alpha \frac{1+\cos \alpha}{1+\sin \alpha}$,
$$
\begin{array}{cc}
\because & a \neq \frac{k \pi}{2}(k=0, \pm 1, \pm 2, \cdots), \\
\therefore & T>0 .
\end{array}
$$

Therefore, the answer is $(C)$.