1. In $\triangle A B C$, if $a^{2}+b^{2}=6 c^{2}$, then the value of $(\cot A+\cot B) \tan C$ is ( ).
(A) $\frac{1}{5}$
(B) $\frac{2}{5}$
(C) $\frac{1}{7}$
(D) $\frac{2}{7}$
-1.B.
In $\triangle A B C$, we have
$$
\begin{array}{l}
(\cot A+\cot B) \tan C \\
=\frac{\sin (A+B)}{\sin A \cdot \sin B} \cdot \frac{\sin C}{\cos C}=\frac{\sin ^{2} C}{\sin A \cdot \sin B} \cdot \frac{1}{\cos C} \\
=\frac{c^{2}}{a b} \cdot \frac{2 a b}{a^{2}+b^{2}-c^{2}}=\frac{2 c^{2}}{a^{2}+b^{2}-c^{2}} \\
=\frac{2 c^{2}}{6 c^{2}-c^{2}}=\frac{2}{5} .
\end{array}
$$