SoulfulSurvivor's advice to you is spot on. However, in case it needs reinforcing, I'll put in my two cents.
This guy is a BS artist. He has proven that to you time and time again. Deep down you know it, too. That's why you are considering going as far as installing a camera at home. Please note --- If you mistrust someone that much, then it's time to get out of the relationship.
Giving someone like him "more sex" won't matter. He'll still go out and cheat on you. Another thing to consider---if you are having unprotected sex with him, you are putting your health at risk.
SoulfulSurvivor mentioned codependency. Take a look at the website of Codependents Anonymous: http://www.coda.org/