sinx/(1-cosx)=(1+cosx)/sinx

Verify Trigonometry Identity.

Operate left side.
sin x / (1 - cos x)
= sin x / (1 - cos x) [(1 + cos x) / (1 + cos x)] ← Rationalize.
= sin x (1 + cos x) / (1 - cos² x)
= sin x (1 + cos x) / sin² x
= (1 + cos x) / sin x
Proven.

sin x / (1 - cos x) = (1 + cos x) / sin x is true.