theorem :: FDIFF_9:41

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