Hello, I am trying to prove this identity: (cscx-cotx)^2=(1-cosx)/(1+cosx)

currently I am did these steps:

(csc(x) - cot(x)) (csc(x) - cot(x)) = (cscx-cotx)^2=(1-cosx)/(1+cosx)

csc^2(x) - 2cot(x)csc(x) + cot^2(x) = (cscx-cotx)^2=(1-cosx)/(1+cosx)

(1/sin^2(x)) - 2(cos(x)/sin(x))(1/sin(x)) + (cos^2(x) / sin^2(x)) = (cscx-cotx)^2=(1-cosx)/(1+cosx)

(1 - 2cos(x) + cos^2(x)) / sin^2(x) = (cscx-cotx)^2=(1-cosx)/(1+cosx)

Now I am stuck :S

please help and thanks!