Is it true that drinking a glass of apple juice before a bikini wax or plucking your eyebrows helps to dull the pain?
If so, how?
Unless you unintentionally left out the word “fermented” between the words “of” and “apple juice” the answer would be no.
I doubt apple juice would have any sort of effect other than as a placebo. However, apple juice does taste yummy-yum-yum, AND, according to my old P.E. coach, can help clean out your digestive tract.
My WAG would be that it gives your blood sugar a quick jolt, thus making you feel better for a few minutes and more able to deal cheerfully with the resultant “discomfort” (they don’t call it “pain”, do they?) 
I personally find it hard to believe, but a friend of my daughter swears that they taught her that in beauty school. I have since asked around and it seems like her school isn’t the only one teaching it.
Isn’t fermented apple juice called apple cider?