An inductor (one coil) will change power factor, as will a capacitor. I was talking about the inability of a transformer to change an input frequency into a different output frequency.
The phase angle relationship between primary and secondary in a transformer is variable, too, by changing the nature of the load(s).
True.
What transformers can do (and in fact, are physcially destined to do)...
I misread "destined" as designed to do...