If the self-induced EMF in an inductor is 180° out of phase with source voltage, shouldn't they cancel out and net voltage should become zero?
If it wasn’t for the fact that the inductor produced a back emf, it might as well be a lump of copper across your signal generator output and then it would be a dead short and you would see no waveform. So, the inductor is doing two things; taking a current from the signal generator and simultaneously producing a back emf.

Most engineers biggest difficulty is understanding how any current can flow when the back emf exactly equals the applied voltage. Regard it as a separate path inside the inductor if you want.


  How can I see both induced emf and source waveform


If you put another winding around your inductor with the same number of turns onto the coil’s core in the same position as the original coil then you would see the back emf across that new winding.