12 Given $\frac{1-|\cos x|}{1+|\cos x|}=\sin x$, then $x=$ $\qquad$ .
(12) $k \pi, 2 k \pi+\frac{\pi}{2}(k \in \mathbf{Z}) \quad$ Hint: $\frac{1-|\cos x|}{1+|\cos x|}=\sin x \Rightarrow \sin ^{2} x=$ $\sin x(1+|\cos x|)^{2} \Rightarrow \sin x=0$, or $\cos x=0$ and $\sin x=1 \Rightarrow x=k \pi$, $2 k \pi+\frac{\pi}{2}(k \in \mathbf{Z})$.