3. Let $a \neq \frac{k \pi}{2}(k=0, \pm 1, \pm 2, \cdots), T \equiv \frac{\sin a+\tan a}{\cos a+\cot a}$.
(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
(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 $\left.a \neq \frac{k \pi}{2}, k=0, \pm 1, \pm 2, \cdots\right)$).