3. Let $\alpha \neq \frac{k \pi}{2}(k=0, \pm 1, \pm 2, \cdots)$.
$$
T=\frac{\sin \alpha+\tan \alpha}{\cos \alpha+\cot \alpha} .
$$
(A) $T$ takes negative values;
(B) $T$ takes non-negative values;
(C) $T$ takes positive values;
(D) $T$ can take both positive and negative values.
3. (C)

Making an identity transformation, we easily get
$$
T=\frac{\sin \alpha+\tan \alpha}{\cos \alpha+\cot \alpha}=\frac{\tan \alpha(\cos \alpha+1)}{\cot \alpha(\sin \alpha+1)}=\frac{\left(\tan^{2} \alpha\right)(\cos \alpha+1)}{\sin \alpha+1}>0 .
$$
(where $\alpha \neq \frac{k \pi}{2}, k=0, \pm 1, \pm 2, \cdots$ ).