3. Let $\alpha \neq \frac{k \pi}{2}(k=0, \pm 1, \pm 2, \cdots), T=\frac{\sin \alpha+\tan \alpha}{\cos \alpha+\cot \alpha}$, then
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
$$
T=\frac{\sin \alpha+\tan \alpha}{\cos \alpha+\cot \alpha}=\frac{\sin ^{2} \alpha \cos \alpha+\sin ^{2} \alpha}{\cos ^{2} \alpha \sin \alpha+\cos ^{2} \alpha}=\frac{\tan ^{2} \alpha(1+\cos \alpha)}{1+\sin \alpha}>0,
$$

Thus, $T$ takes a positive value, so the answer is $C$.