If the output voltage of two transformers are 180 degrees out of phase, the problem could be due to and simply resolved either by cutting or swapping the wires to the 120 volt input male plug on the transformer to reverse the polarity or by filing down the slightly wider prong on the male plug to fit the slightly smaller female slot on the 120 volt outlet or by using an intermediate 2 prong 3 wire adapter.
WARNING
Although any above solution will work electrically, it would be considered unsafe by an Electrical inspector in case of fire. As a 1960 graduate BSEE (Electrical Engineer) with over 50 years of experience in the Electrical Utility Industry, I would recommend the following:
BETTER IDEA
Use a voltmeter to measure that the "hot" smaller slot of every 2 pole 120 volt outlet is 120 volts to ground and "neutral" slightly wider slot is at zero potential to ground.
Reference ground could be either the round slot on a three prong 120 volt outlet, or the screw to metal cover plate on a metal outlet box or other nearby grounded metal water pipe. If the polarity to the 120 volt outlet is discovered to be incorrect, one should then disconnect power to the 120 volt outlet and visually check wiring to the outlet.
According to the NATIONAL ELECTRICAL CODE, the "hot" black (or sometimes red) wire should always be connected to the brass screw (which is internally connected to the smaller slot of the 120 volt outlet) and the "neutral" (usually white) wire should be connected to the silver screw (which is internally connected to the slightly wider of the two straight slots of any 120 volt outlet).
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