theorem :: FDIFF_11:50

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))) + ((2 * (cosec . x)) / (1 + (x ^2))) ) )