Amplitude spectra of cos product
Use your trigonometric identities, such as:

$$cos(A) cos(B) = \frac 1 2 (cos(A + B) + cos(A - B))$$

In your case, this woks out to:

$$cos(2\pi t) cos(20\pi t) = \frac 1 2 (cos(2\pi t + 20\pi t) + cos(2\pi t - 20\pi t))$$

$$ = \frac 1 2 (cos(22\pi t) + cos(-18\pi t))$$

Since \$cos(x) = cos(-x)\$, you can also write this as

$$ = \frac 1 2 (cos(22\pi t) + cos(18\pi t))$$

If you factor out the \$2\pi t\$ from each argument, this means that you have two new signals, at 9 Hz and 11 Hz, each half the amplitude of the original signals.