$7 \cdot 76$ Among the following four functions, which one is both an even function and a periodic function?
(A) $|\sin x|$.
(B) $\left|\log _{2} x\right|$.
(C) $\sin |x|$.
(D) $\log _{2}|x|$.
(2nd "Hope Cup" National Mathematics Invitational Competition, 1991)
[Solution] Since $\left|\log _{2} x\right|$ and $\log _{2}|x|$ are both non-periodic functions, options $(B)$ and $(D)$ are eliminated. Noting that the graph of $(C)$, as shown in the figure, is also not a periodic function.

Therefore, the answer is $(A)$.