Prove that 1-sinx/1-secx - 1+sinx/1+secx = 2cotx(cosx-cosecx)

step by step pleeasseee

(1 - sin x) / (1 - sec x) - (1 + sin x) / (1 + sec x)
= [(1 - sin x)(1 + sec x) - (1 + sin x)(1 - sec x)] / [(1 - sec x)(1 + sec x)]
= [1 - sin x + sec x - tan x - 1 - sin x + sec x + tan x] / [1 - sec^2 x]
= [2 sec x - 2 sin x] / [1 - 1 - tan^2 x]
= 2(sin x - sec x) / tan^2 x
= 2 cot x (sin x - sec x) (cos x / sin x)
= 2 cot x (cos x - cosec x).