theorem :: FDIFF_9:23

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