Fourier representation of CT peridic signals

I am looking for the Fourier coefficients for the following signal:
(cos(2pi*t))^2

Please tell me if my logic is correct.

I use the trig identity to get
(1/2) + (cos(2pi*t)/2

I use the complex definition to get
(1/2) + (1/4)(exp(j2pi*t) + exp(-j2pi*t))

I then use the synthesis equation to get the following coefficients
a_0 = 1/2, a_1 = 3/4

Thanks