If two coils have the same magnetic flux in common, and they have the same number of turns, then the emf generated in each is the same. If you neglect parasitic effects, such as the resistance of the coils, and assuming the there is no core saturation or other fact that brings non-linearity into the picture, then if you apply an alternating voltage source across one coil, which is for that reason called the primary, then a back emf must be generated by changing flux in that coil that matches the applied emf. (Suppose that were not the case. Then, the current in the coil would have to increase, which, in turn would cause the back emf to rise). But since that back emf in the primary is also common to the other coil, then the same emf must be generated in the other coil, i.e. the secondary.
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