Finding Fourier coefficients

[dimon]

Hello
I am trying to find Fourier coefficients for x(t) = 4cost(t)cost(4t)
I'm just learning this and do not completely understand even after reading the definition a couple of times.

This is what I have so far:

applying Euler's identity i got: [e^it + e^(-it)] [ e^4it + e^(-4it) ]

This is where I'm stuck. Any help would be appreciated.

 

[royhaas]

Use the identity \(\displaystyle cos(X+Y)+cos(X-Y) = 2cos(X)cos(Y)\).