The value of , assuming a is always a nonzero integer, will always equal 1, since sine is a periodic function. Go on, try it. So, he or she basically just canceled out 1 and 1 from the fraction.
Not quite... Depending on the remainder in the division of by 4, can take the values 0, 1 or -1. Go on, try it .
In the present case, the explanation is that and for any (i.e. sine is periodic, with period ). (By the way, ).