I think the answer to this question will truly depend on what you're fighting about and why your husband doesn't trust you. Without knowing these things, I'll do my best to answer.
The best way to earn someone's trust is not by saying "Trust me!" or having repeated emotional conversations. It's by follow-through.
If your goal is to get him to trust you, you should try and be a little more transparent. For example, if you have social media accounts he doesn't know about, tell him about them.
If you tell him you're going to be somewhere, be there.
If you say you're going to call him at X o'clock, call him!
Only time can encourage trust.
There's a great article about rebuilding broken trust that I think you'll find interesting. The article is found here: https://www.marriage.com/advice/infidelity/5-tips-for-restoring-trust-after-infidelity/ and has some great advice on how to make your marriage healthy again.