I have a question regarding medical examinations which requires patients to reveal their private parts to the doctor.What is the ruling on a man who revealed his private parts to a woman doctor, only for the intention of medical examination?..the man is a Muslim and the woman is Christan. The man did not have any previous knowledge about the ruling of such action in islam. But now he is very shamefull and does not know what to do to repent from this bad deed.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Exposing one's Awrah to anyone other than his wife is forbidden as reported by Ahmad from Bahz Ibn Hakim that his grandfather said to the Messenger of Allah: "What of our Awrah (for the man from navel to knee and for the woman her whole body) should we conceal from others and what should we expose?" He said to him: "Conceal your Awrah except from your wife or your slave woman". He (the grandfather) said: "What if the people are all mingling (in a gathering)". He said: "If you can conceal it from everybody do that". He (the grandfather) said: "what if one of us is alone?" The Prophet (Sallallahu Alaihi wa Sallam) said: "Allah has more right on us to be shy of Him" .
This if there is no dire necessity. But if there is necessity to expose one's Awrah such as getting treated from an illness that cannot be cured otherwise and provided that each sex gets treated by doctors from similar sex unless there are no such doctors. So, if there is only this female doctor, in your case, there is no harm that you get treated by her provided you do not stay with her in seclusion. Now, that you have exposed your Awrah to this lady out of ignorance, we hope that Allah will forgive this sin as you did not know the rule.
Allah knows best.