Finding Fourier series for function $f(t) = \cos 3t \cdot \sin 5t$ in complex form.

Question

I have no idea how to go about it, because of the $\sin$ and $\cos$ terms being multiplied. I tried using Euler's Identity to separate them from each other but then I am stuck on: $$f(t)=\left(\frac{e^{3tj}+e^{-3tj}}{2}\right)\left(\frac{e^{5tj}-e^{-5tj}}{2j}\right)$$

Answer 1

The best way is to use the indentity

$$\sin(\alpha) \cos(\beta)=\frac{1}{2}( \sin(\alpha +\beta) +\sin(\alpha -\beta) ) $$