Question

Establish the identity:
(1+cos x)/sinx = sinx/(1-cos x)

Answer 1

by "establish the identity" do you mean prove? or to find a trig identity given that?

Answer 2

if it's the latter you can just cross multiply

(1+cos x)(1 - cos x) = (sin x)(sinx)
simplify
1 - cos^2x = sin^2x
add cos^2x to both sides
1 = sin^2 x + cos^2 x

this is the pythagoran identity