What can i do to get him to trust me?

i’ve been going out with my boyfriend for about 6 months now. He doesn’t trust me because in the past, i cheated on my exboyfriend and now my boyfriend thinks i’ll do the same on him.
but i’ve given him no other reason to think i’ll look for anyone else.
how can i get him to start trusting me? it’s been six months and it’s really hard to be in a relationship with no trust.
i’ve been really sweeet to him, he even says so, but i think his ex made him bitter towards women…
i want to try and fix everything, but i don’t even know where to begin. especially since technically, there’s nothing wrong. i’ve done NOTHING!