verify the identity

Question

((cosxcotx)/(1-sinx))-1=cscx

Answer 1

((cosxcotx)/(1-sinx))-1=cscx

(cos x*cos x/sin x) /(1-sin x) = 1 + 1/sin x

(cos^2 x)/[sin x *(1-sin x)] = (sin x+1)/sin x

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

cos^2 x = (1-sin x)(1+sin x)

cos^2 x = 1 - sin^2 x
sure does