how does a phase shifting transformer work?

Question

this is a power transformer

Answer 1

All transformers phase shift.
A transformer is two coils inductively coupled.
AC is fed into the primary coil and AC comes out the secondary coil 90 degree phase shifted .
An induced voltage is proportional to the rate of change of the magnetic field around the wire.
A magnetic field around a wire is proportional to the current flowing in the wire.
This magnetic field is re-enforced by wrapping the wire into a coil.

When the current in the primary coil is changing quickly (i.e. when going up or down from the sine wave's valleys and peaks ) the magnetic field is also changing its fastest. This induces the most voltage in the secondary.
When the current in the primary coil is changing slowly (i.e. when going over the sine wave peaks and valleys) the magnetic field is also changing its slowest. This induces the least voltage in the secondary.
This shows up as a cosine wave in the secondary to the sine wave in the primary.