Consider the following three continuous-time signals with a fundamental period of T = 1/2

x(t) = cos(4*pi*t)

y(t) = cos(4*pi*t)

z(t) = x(t)y(t)

a) Determine the Fourier series coefficients of x(t).

b) Determine the Fourier series coefficients of y(t).

c) Use the results of parts a and b along with the multiplication property of the CT Fourier series to determine the Fourier coefficients of z(t).

d) Determine the Fourier series coefficients of z(t) through direct expansion of z(t) in trig form and compare that with the results of part c. (I'm guessing they will be equal.)

What I have so far:

I think I have to use these trig identities.

Also, I know the definition of the fourier series coefficients a0, an, and bn.

x(t) = a0 + \[\sum\]an\[\times\]cos(2\[\times\]pi\[\times\]n\[\times\]t/T) + \[\sum\]bn\[\times\]sin(2\[\times\]pi\[\times\]n\[\times\]t/T)

Aside from that, I'm pretty much lost. Any suggestions?