163 The number of solutions to the equation $\sin |x|=|\cos x|$ in the closed interval $[-10 \pi, 10 \pi]$ is $\qquad$ .
163 20. Since $\sin |x|$ and $|\cos x|$ are both even functions, we only need to consider the number of solutions within $[0,10 \pi]$, at which point the equation becomes $\sin x=|\cos x|$. When $0 \leqslant x \leqslant \frac{\pi}{2}$, the equation becomes $\sin x=\cos x$, with only one solution $x=\frac{\pi}{4}$; when $\frac{\pi}{2} \leqslant x \leqslant \pi$, the equation becomes $\sin x=-\cos x$, with only one solution $x=\frac{3 \pi}{4}$, so $\sin x=|\cos x|$ has 2 solutions within $[0,2 \pi]$, thus $\sin |x|=$ $|\cos x|$ has $10 \times 2=20$ solutions within $[-10 \pi, 10 \pi]$.