Now modulate this carrier with another frequency: B*sin(phi*t). B is the amplitude and phi is the frequency of the modulation.
What is the result? The two waves will be added point by point. The result will be A*sin(omega*t) + B*sin(phi*t).
We want to know what happens when phi gets close to omega. So we keep omega constant and change phi from omega-alpha to omega+alpha where alpha is a number of the order or greater than omega. That means we scan over the frequency like a radio tuner.
Just assume (else it will be messy to write) A=B=1; then sin(omega*t)+sin(phi*t)=2*sin((omega+phi)*t/2)*cos((omega-phi)*t/2)