题目

Farmers are being told more needs to be done to stop them injuring  at work.One in five British workplace deaths happens in agriculture  even though farmers are only a small part of the working population.During the year 2010/11 there were 1,061 injuries in total and it is thought many more go unreported. Jim Chapman from Warwickshire had his arm torn off by farm machinery seven years ago when he was 23.“You don't realize how  much you rely on your second arm until it's gone，”he said.He fell against a PTO shaft(传动轴)，a spinning metal bar at the back of  a tractor.“It如图，在梯形ABCD中，AB∥CD，AD=DC=CB=a，．∠ABC=60°，平面ACFE⊥平面ABCD，四边形ACFE是矩形，AE=a，点M在线段EF上．（1）求证：BC⊥平面ACFE；（2）当EM为何值时，AM∥平面BDF？证明你的结论；（3）求二面角B-EF-D的平面角的余弦值．