theorem :: FDIFF_11:49

for Z being open Subset of REAL st Z c= dom cosec & Z c= ].(- 1),1.[ holds
( cosec (#) (arctan + arccot) is_differentiable_on Z & ( for x being Real st x in Z holds
((cosec (#) (arctan + arccot)) `| Z) . x = - ((((arctan . x) + (arccot . x)) * (cos . x)) / ((sin . x) ^2)) ) )