Fourier Transform of $\cos(\pi t)+2\sin(3\pi t)+\cos(5\pi t)\cos(7\pi t)$ I think I understand this question up until the last term. So far I have: $$F(\omega)=\pi(\delta(\omega+\pi) + \delta(\omega-\pi))+2\pi(\delta(\omega+3\pi) + \delta(\omega-3\pi))+\frac{1}{2}(\delta(\omega+5\pi) + \delta(\omega-5\pi)*\delta(\omega+7\pi) + \delta(\omega-7\pi))$$ I don't understand how to convolve the delta functions. Let me know if I am on the right track with this. Thank you!

There's no need to convolve the delta functions, because

$$\cos{5 \pi t} \cos{7 \pi t} = \frac12 (\cos{2 \pi t} + \cos{12 \pi t})$$