Question regarding Frequncy component

Lets suppose we are having two cos functions having frequency 500 Hz and 250 Hz. when these cos function are multiplied to make a single signal, the frequency spectrum shows frequency components at 750 Hz and 250 Hz

Now the minimum sampling freq for this signal(which is being multiplied) will be 1500 Hz. Is this true

Answer 1

[Wayne King]

Yes, that's correct there will be frequency components at [-750 -250 250 750] so the bandwidth is 1500 Hz, you have to sample at least at 1500 Hz.