the reason for using transformer in dual output power supply?

Answer 1

Even most single output power supplies have a transformer.

A center-tapped secondary on a transformer makes it easy to create a dual voltage at the output (+ and - voltages). All you need is a bridge rectifier and 2 capacitors for the basic part of the DC outputs. The center-tap of the secondary of the transformer becomes the common (ground) terminal for the dual supply.
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Answer 2

to make sure that the in flow of electricity is equal to that being able to consume by the supply. If the outlet is 120 volts, and the your stereo is European produced 200 or so, then you need a transformator, to make it balanced. its useful.