In my book following result is shown but don't know where it come from.

1.2cos^2(2kpie)=2 (where k is an integer)

2.cos(kpie)=(-1)^k

3.[sin(kpie)cos(theta)-cos(kpie)sin(theta)]=[(-1)^k-1 sin(theta)]

In all these cases I just don't know how the results came.Please explain it to me.