答案：B
$\begin{array}{rcl}
\cos^2 x – \sin x & = & 1 \\
(1-\sin^2 x) – \sin x -1 & = & 0 \\
-\sin^2 x -\sin x & = & 0 \\
\sin x( \sin x – 1) & = & 0
\end{array}$
$\begin{array}{rcl}
\cos^2 x – \sin x & = & 1 \\
(1-\sin^2 x) – \sin x -1 & = & 0 \\
-\sin^2 x -\sin x & = & 0 \\
\sin x( \sin x – 1) & = & 0
\end{array}$
所以，$\sin x =0$ 或 $\sin x = 1$。
由此，可得 $x=0^\circ$、$x = 180^\circ$ 或 $x=90^\circ$。
所以，方程有 $3$ 個根。
