2. In $\triangle A B C$, $a^{2}+b^{2}=7 c^{2}$. Then $(\cot A+\cot B) \tan C=(\quad)$.
(A) $\frac{1}{3}$
(B) 3
(C) -3
(D) $-\frac{1}{3}$
2.A.
$$
\begin{array}{l}
(\cot A+\cot B) \tan C=\left(\frac{\cos A}{\sin A}+\frac{\cos B}{\sin B}\right) \frac{\sin C}{\cos C} \\
=\frac{\sin (A+B) \cdot \sin C}{\sin A \cdot \sin B \cdot \cos C}=\frac{c}{a} \cdot \frac{c}{b} \cdot \frac{2 a b}{a^{2}+b^{2}-c^{2}} \\
=\frac{2 c^{2}}{a^{2}+b^{2}-c^{2}}=\frac{1}{3} .
\end{array}
$$