根据短文内容，完成下列小题。

    During the summer holidays there will be a new schedule(时间表).

    Changes for meal and library service hours and for bus schedules will be shown on the wall outside the dining room. Weekly film and concert schedules, which are being made, will be shown each Wednesday outside the library.

    Buses to the town center will leave the North Beijing every hour on the half during the day. The dining room will serve three meals a day from 7:00 a.m. to 7:00 p.m. during the weekdays and two meals from noon to 7:00 p.m on weekends. The library will continue its usual hours during the weekdays, but have shorter hours on Saturdays and Sundays. The weekend hours are from noon to 5:00 p.m.

    All students who want to use the library borrowing service must have a new summer card. This announcement(通知) will also be shown in the next week's student newspaper.

在函数①y=cos丨2x丨，②y=丨cosx丨，③y=cos（2x+$\frac{\mathrm{\pi }}{6}$）④y=tan（2x﹣$\frac{\mathrm{\pi }}{4}$）中，最小正周期为π的所有函数为（　　）

如图，已知点D为等腰直角△ABC内一点，∠CAD＝∠CBD＝15°，E为AD延长线上的一点，且CE＝CA.

(1)求证：DE平分∠BDC；
(2)若点 M在DE上，且DC＝DM，求证：ME＝BD.