Can you date someone with trust issues?

My boyfriend has trust issues from previous relationships which he has admitted to me. He gets easily jealous and kind of controlling at times, but he says that he’s not. We’ve been together for 6 months now and he still doesn’t trust me. I know that we need to work on our communication, but there is no reason not to trust me. He doesn’t like when I go out with my friends, he checks up on me every time we’re not together, when we’re apart he calls me multiple times a day just to talk, and he’s low-key anxious when I go out without him. He once accused me of cheating because I texted him instead of sending pictures when I was out with my friend. It feels like he always needs to keep an eye on me even if i’m not doing anything. He always wants to know where i’m at and who i’m with and what we’re doing. At times it has been exhausting always having to explain myself and keep him updated because I sometimes feel like I can’t enjoy myself because I know that he will think that something is wrong. I don’t know how to proceed or how to gain his trust. Or if it’s even worth it. I’m not sure if things will change because they haven’t changed this far in our relationship.

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