How would you simplify and prove (csc x - cot x) = (1-cos x)/(1+cos x)? I've tried a lot of different starts, but I keep getting stuck.
One of the first things you should do when proving identities is to make sure they are true by taking any value of the angle.
I tried 45 degrees and
Left side = .707106 - 1 = -.2928...
right side = (1-.707)/(1+.707) = .17...
No wonder you could not "prove" it, the equation is not an identity.