Trust is an evolving entity. U don't have to trust him with the same situation, but the forgiveness is actually for u. You will feel and do better if ur not wasting energy holding a grudge. Let him lose some trust and try to earn it back. But forgive him so it doesn't eat at u.
Not knowing what he did, it makes it hard to know how to answer. I think almost everyone deserves a second chance but I also think he is the one that needs to prove himself worthy of you. Whatever you decide to do, do it now. Letting an issue this serious just set around only makes it harder to deal with....get it out and get it over with.
See if he is truly sorry by trying to make it up to you. If he does try to rebuild the trust and make you comfortable with the situation, then give him another chance. If he repeats the deceit, then decide whether you can be with a dishonest mate.