3. The number of real roots of the equation $x=\sin x+1993$ is ( ).
(A) 0 .
(B) 1 .
(C) 2 .
(D) Greater than 2 .
3. (B).

Since the roots of the equation are the x-coordinates of the intersection points of the line $y=x$ and the curve $y=\sin x +1993$, the equation has at least one real root.
Assume the equation has two distinct roots $x_{1}, x_{2}, x_{1} \neq x_{2}$, then
$$
\begin{array}{c}
x_{1}=\sin x_{1}+1993, \quad x_{2}=\sin x_{2}+1993 . \\
x_{1}-x_{2}=\sin x_{1}-\sin x_{2} \\
=2 \sin \frac{x_{1}-x_{2}}{2} \cos \frac{x_{1}+x_{2}}{2} .
\end{array}
$$

Since $\left|\sin \frac{x_{1}-x_{2}}{2}\right| \leq 1$ and $\left|\cos \frac{x_{1}+x_{2}}{2}\right| \leqslant 1$, this leads to a contradiction.
Therefore, the original equation has only one real root.