How do I convince my boyfriend that I'm not cheating on him?

I've been with my boyfriend for about 4 months. He's a lovely guy, really affectionate, and we have a great time together. The downside - he dislikes my male best friend. I don't know why. My friend always stays civil with my boyfriend whenever he sees him. I have also known my friend since we were like 5.

My boyfriend went away on holiday last week and I went out with some friends. My friend got drunker than usual (he was sick) and he also lives really far away, so I said he could stay in my spare room. I told my boyfriend as I didn't see it as a big deal and I never hide anything, and he got really angry. He went off on a rant saying that I was seeing my friend behind his back and that having him sleep over was proof.

So what the hell do I do? I don't think I acted inappropriately. This is really annoying me that he doesn't trust me.
How do I convince my boyfriend that I'm not cheating on him?
Post Opinion