Why is there a Half Cos(x) Term in the Fourier Series for Cos(x)?

[Osmano]

Hello, I'm having some trouble completing a Fourier series question.

We have f(x)=Cos(x), for abs(x)≤π/2
f(x)=0, for π/2≤abs(x)≤π
period=2π

and then show that the Fourier series f(x) reads
http://img71.imageshack.us/img71/3424/84335314oi1.jpg
now I can get the 1/π and the sum, as a_n=
http://img71.imageshack.us/img71/1703/eq2hn6.jpg
and working through from there, the only part I'm having trouble with is the origin of the half cos(x) term. As far as I'm able to apply the Fourier series I don't see where it comes from. (B_n must equal 0 right?)

 

[neo86]

How did you deduce, that the Bn are zero? The orthogonality relation between sin and cos only holds if you integrate from 0 to 2pi, but in this case you integrate only from 0 to pi/2.