theorem :: FDIFF_9:44

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