In a transformer, let's say we have:
I1, I2 - currents through the primary and secondary winding
V1, V2 - voltages
N1, N2 - number of turns
F1, F2 - magnetic fluxes through core, produced by the currents I1 and I2 (they are opposing...)
R - the reluctance of the core

We have V1/V2 = N1/N2 = I2/I1.
F1=N1I1/R; F2=N2I2/R
I think I1 and I2 are in phase too.
That means F1 and F2 are practically equal.
How can we have a nonzero resulting flux through the core? F=F1-F2
If the flux through the iron core is zero, then the cause that produces V2 (variation of the flux) does not exist, then V2=0?

[Transformer][1] [1]: https://en.wikipedia.org/wiki/Transformer#/media/File:Transformer3d_col3.svg