1. In $\triangle A B C$, $\lg \sin A-\lg \cos B-\lg \sin C=\lg 2$. Then $\triangle A B C$ must be ( ).
(A) isosceles triangle
(B) equilateral triangle
(C) right triangle
(D) shape uncertain
- 1.A.

From the given information, we have
$$
\begin{array}{l}
\left\{\begin{array}{l}
\sin A=2 \cos B \cdot \sin C, \\
\angle A=\pi-(\angle B+\angle C)
\end{array}\right. \\
\Rightarrow \sin (B+C)=2 \cos B \cdot \sin C .
\end{array}
$$

Rearranging, we get $\sin (B-C)=0$.
Thus, $\angle B=\angle C$.
Therefore, $\triangle A B C$ must be an isosceles triangle.