Saying you committed in adultery to a judge, in some states, can mean legal and financial loss during a divorce.
Quoted for emphasis.
Also, in some juristictions it is not legally considered adultery if you have sex with someone after the date of your separation, thus making it none of your ex's business if you're seeing someone now, or if you intend to. Check the laws in your area.
NEVER make yourself look bad so that others can save face. It's never appreciated.
W