Connect C 1D, then △DEC 1 is a right triangle.

Let the side length of the cube be a.

Then C 1D=√2a.

Because e is the midpoint of AD- >; DE = a/2-& gt； C 1E=3a/2

In Rt△C 1ED.

cos∠c 1ED = DE/c 1E =(a/2)/(3a/2)= 1/3

That is, the cosine of the angle between C 1E and BC is 1/3.