For the Forier series whose Period is 2 and f(t) = cos( pie/2 * t)

I have trouble getting the trig identity down.

eventually I reach a_0 = 4 / pie

but once I come to a_n

I cannot understand how to integrate

the integral of [ cos(nt) * cos(pie /2 * t) * dt] from -1 to 1

I have tried integration by parts but to no avail

Thank you for your time