Well, it helps if you really don't care, but I wouldn't recommend it!
What helps me is to close my eyes and simply try to hear the music, or look at some random spot in the ether avoiding eye contact ... I find I'm worse when there are people I know in the audience as opposed to people I've never seen before and despite playing in public for a good decade or so, I still don't like to play solo. I don't mind a duet and a trio is perfect, but I don't do solo well. it's nice to know that about yourself! I learned back in college that teachers are just people who happened to know more than I do, they're not monsters or ogres or the Wrath of God or whatever. I've had a couple students over the years (music and editing) and I always feel bad when they're obviously terrified of me since I'm a pretty non-judgmental sort of educator and still learning myself. So don't put a teacher on a pedestal -- they really are just people.
Also, eat a banana before you go play for an audience (even your teacher). It sometimes helps a lot.
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