Trust is the foundation for every relationship , and if someone has broken your trust i don't think you can get the same level of trust back with that same person. Trust is one of life's most difficult challenges. So i would never give someone a second chance when they have already given me one good reason not to trust them
I'd never waste my time on someone who wasted my faith and trust. I'd leave him so i could heal and then move on. Giving someone a second chance after a betrayal would be giving them the opportunity and your permission to hurt you again, because people only treat you how you allow them to treat you
I cheated on my wife, we broke up for about 8 years and we got back together, and have been happy ever since (13 years now, including some time when we were long distance). I got all of that out of my system, years ago and now I am happy and settled.
By cheating, he has shown a lack of respect for you and how much respect can you really have for someone who has treated you poorly? Sometimes a girl knows the truth about her guy's infidelity but doesn't want to dump him because she's afraid to be alone.
If that's the case, remind yourself that there are far worse things than being single like being with a guy who takes advantage of you. Still, if you want to consider giving this guy a second chance, the first thing you should do is have a heart to heart with him.