Inductors in Transformers Why is it the flux change which induces the ac current of the primary coil equal to the flux change that the primary coil induces on the secondary coil?  Is it possible to prove this?
Reference: https://slideplayer.com/slide/7425627/
 A: 
Why is it the flux change which induces the ac current of primary coil equal to the flux change that primary coil induces on the secondary coil?

Because you're only studying or modeling an ideal transformer.
In a real transformer, flux through the secondary is somewhat less than the flux through the primary. Some of the flux produced by the current through the primary coil goes outside the core, where it doesn't produce any effect in the secondary. We call this the leakage flux. 
Its effect is as if there is an additional inductance in series with the primary, which we call the leakage inductance of the transformer.
A common model for a non-ideal inductor including this effect is this:

Here, $X_{l_1}$ is the primary leakage inductance and $X_{l_2}$ is the secondary leakage inductance. 
$R_C$ and $X_M$ represent additional non-idealities: core losses and magnetizing reactance.
It's also common, for practical circuit design, to transform the secondary leakage inductance across the transformer and represent both leakage inductances with a single parasitic element on the primary side of the ideal transformer.
For well designed transformers, the leakage inductances can be as low as 1-2% of the coupled inductances.
