(personal opinion to follow)
Trust isn't something that "just comes back" it has to be re-earned.
I cheated, I lied, I came clean, I apologized, I changed.
HOWEVER-that doesn't mean all of a sudden because I said I was sorry and I decided to change that trsut was rebuilt.
It's taken years of me being true to my word and showing that "when the going gets tough" I will continue to be honest and forthright-for that trust to be rebuilt.
Now, I will grant-one lie, one time-shouldn't take years to re-earn trust. But, "I'm sorry" doesn't make it happen.
Stop beating yourself up over the fact that like a normal human, you need to SEE a change before you can believe it.
(there's a reason we always say actions speak louder than words)
He's given you the words-that's great. Going to take some time and trials to see if he follows through with the actions.
Anyway-in the meantime, read through some of the blogs on here-there's a wealth of "how I could have managed better" and "how I navigated xyz emotion" in there.
"Love As Thou Wilt"