In that equation of Mr Al for AM, the result is actually "DSB", meaning double-sideband, suppressed carrier.
The difference is when the "baseband" modulating signal goes through zero, the output of that modulator also goes through zero volts.
In AM (double sideband but with carrier), when the modulating signal goes through zero the output is an RF sinusoid whose amplitude ("carrier") is 1/2 the maximum value .
As shown in the animation above, the output level goes from zero (at max negative baseband signal) through "carrier", to maximum output.
True AM is less efficient than the suppressed-carrier versions, but the required demodulation is far simpler (merely following the peak values and filtering out the carrier frequency to obtain the baseband), allowing an elementary "crystal radio" circuit to work.