3. Among the four functions $y=\sin |x|, y=\cos |x|, y=$ $|\cot x|, y=\lg |\sin x|$, the one that is periodic with $\pi$, monotonically increasing in $\left(0, \frac{\pi}{2}\right)$, and an even function is ( ).
(A) $y=\sin |x|$
(B) $y=\cos |x|$
(C) $y=|\cot x|$
(D) $y=\lg |\sin x|$
3.(D).
$y=\sin |x|$ is not a periodic function. $y=\cos |x|=\cos x$ has a period of $2 \pi$. $y=|\cot x|$ is monotonically decreasing on $\left(0, \frac{\pi}{2}\right)$. Only $y=\lg |\sin x|$ satisfies all the conditions.