Problem 629

(C)
3. 【Analysis and Solution】By making an identity transformation, we easily get
$$T=\frac{\sin a+\tan a}{\cos a+\cot a}=\frac{\tan a(\cos a+1)}{\cot a(\sin a+1)}=\frac{\left(\tan ^{2} a\right)(\cos a+1)}{\sin a+1}>0 \text {. }$$
(Where $\left.a \neq \frac{k \pi}{2}, k=0, \pm 1, \pm 2, \cdots\right)$).