His indiscretion is still fresh in your mind and what you both have to realize is that it's going to take some time for you to get the trust back and it's not going to happen overnight. Maybe this time will help you to not only trust him again but make your relationship better and stronger. The living apart may be a blessing because if you were to have to be around him everyday it might be a constant reminder of his cheating and you would fight and ultimately the relationship would end. To be able to trust each other again will require an attitude adjustment. You can save the relationship, but it will take some hard work and you will have to start with building trust in each other again. To gain trust, you must fix the original problem for the relationship to work again and find out what went wrong to make him cheat. If you cannot do it on your own, you may need to go to counseling for couples to work it out.
In order for your boyfriend to gain your trust back he has to make small promises and then show you that he can keep them. Try to find something positive in the past and move forward in the relationship into the future. Show him that you are trying to get the trust back even if you are finding it hard to do and show him that you now understand how much you really love him and want to support him. This can actually help you to grow closer and the relationship to grow deeper. Your boyfriend has to make a plan to get your trust with small steps at a time and be patient. It will take time and the relationship can be healed if you have a good solid plan and you change his actions match his words.