theorem :: FDIFF_8:25

for Z being open Subset of REAL st Z c= dom ((- cot) - (id Z)) holds
( (- cot) - (id Z) is_differentiable_on Z & ( for x being Real st x in Z holds
(((- cot) - (id Z)) `| Z) . x = ((cos . x) ^2) / ((sin . x) ^2) ) )