Welcome to PC.
Try not to think of yourself as a burden. Your friend seems very understanding and has offered. For all you know it may help him very much. Often when we tell what is really going on it helps others in ways we can't even imagine. Sharing your story here is not a burden, it helps me and others. We are in this thing together.

Coping strategies. My first thought is let yourself be sad. If you are sad you are sad, there is no shame in that. My second thought is why are you sad and like you said you don't know. There are lots of coping strategies. One that comes to mind is cognitive behaviour therapy. You have to practice a lot of self awareness and it takes practice. But try to be aware of what you are thinking about before you get sad. If you can pinpoint thoughts that may cause it you can challenge them. If they are bubbling up from the sub conscience and you are not aware of them then it is more challenging. You could start practicing meditation which really helps you to become more self aware.

How long have you been feeling this way?