As far as I correctly understand your question, the signals to the primary coil are rectified, that means they are A*|sin(wt)| and A*|sin(wt+90)| (I supposed same amplitude).
In this case the 45 degrees shift still apply, but the sum will have an amplitude going from A to sqrt(2)*A. This can be seen just applying the sum to the first 90 degrees (after the rectifier the frequency will double), then the waveform will repeat. In the first 90 degrees both sin(wt) and sin(Wt+90) are positive, then:
A*|sin(wt)| + A*|sin(Wt+90)| = A*sin(wt) + A*sin(wt+90)