Solution: Take the midpoint E of AA 1 and the midpoint F of C 1D 1 as shown below, and connect ED, EN, DF and MF.

So from NE‖AB, AB‖CD, we get NE‖CD, and NE=CD, then the quadrilateral ENCD is a parallelogram.

in this way

Similarly, AM‖DF is easy to obtain,

So ∠EDF is the included angle formed by straight lines AM and CN in different planes,

In △EDF, it is easy to get ED=DF=√5/2 and EF=√6/2.

According to the cosine theorem, cos∠EDF=(2*5/4-3/2)/2*5/4=2/5.

The title is unclear. If it is the cosine of the angle formed by two straight lines in different planes, then the answer is two? 2/5 or -2/5,

If it's the cosine of the angle, just one? , or 2/5.

The EF value was miscalculated just now. sorry