theorem Th13: :: INTEGR14:13

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