How to answer this trigonometry ecuation

( sec x - tan x) (csc x + 1) = cot x

sec(x) = 1/cos(x)
csc(x) = 1/sin(x)
cot(x) = 1/tan(x)
tan(x) = sin(x)/cos(x)
so:
( sec x - tan x)
= (1/cos(x) -sin(x)/cos(x)
=(1 -sin(x))/cos(x)

(csc(x) +1)
= 1/sin(x) + 1
=(1 +sin(x))/sin(x)

so:
( sec x - tan x) (csc x + 1)
=(1-sin(x))(1 +sin(x))/(sin(x)cos(x)
= (1- sin^2(x))/(cos(x)sin(x))
= cos^2(x)/(cos(x)sin(x))
= cos(x)/sin(x)
=cot(x)