Do you have any reason to believe he is cheating on you? I would recommend being open with who you are with. Sometimes it sounds much easier that it is especially if you do not already have great communication. Can both of you talk about everything together?

You could always spy on them, but is it really worth it? I always think that a relationship needs changing if there is no trust. That does not mean that you necessarily need to break up - it only means that you need to change something to get that trust back.

Does your boyfriend trust you? I have always told my girlfriends in the beginning that if they ever had feelings for anyone else, just let me know so we can part ways and keep that trust there instead of going behind my back and cheating which is never fun to go through.

If you really care about this person, feel them out, try to talk, but I would not recommend spying on them or doing anything that breaks the trust unless you have a great reason to or some type of evidence that something is going on. What it really comes down to though is that you know your relationship better than anyone, and I trust that you will make the decision that you need to make.

I hope this helps! Let me know how it goes!