Modulation is a technique which modifies waves of high frequency by the wave of low frequency.
Consider the carrier signal:
the modulating signal:
and the signal after modulation look like
Putting this all together gives
Now multiply the terms with cosines by :
and substitute with - the amplitude modulation index.
The sideband components are
The single-sideband transmission reduces the bandwidth transmitted and it allows to double the number of channels within the same frequency band.