108 The number of real roots of the equation $1-\lg \sin x=\cos x$ is
A. 0
B. 1
C. 2
D. Greater than 2
108 A. Since for all $x$ in the domain, $\lg \sin x \leqslant 0, 1-\lg \sin x \geqslant 1$. Therefore, $1-\lg \sin x$ $\geqslant \cos x$. The equality holds only when $\sin x=\cos x=1$. However, this is impossible, so the original equation has no solution. Hence, the answer is A.