i cannot prove this no matter what i try to do! I need help to be able to pass my test tommorrow.

Prove sin(t)/(1-cos(t)) = (1+cos(t)) / sin(t)

I worked with the left terms:

sin(t) / (1-cos(t)) | Problem

sin(t) / (sin^2(t) + cos^2(t)-cos(t)) | Pythagorean ID:sin^2(t) + cos^2(t) = 1

what to do next? i already tried seperating all the terms and that doesn't work out. I have a test tomorrow on this stuff and i really need some help.