theorem :: FDIFF_8:22

for Z being open Subset of REAL st Z c= dom (tan + (cos ^)) & ( for x being Real st x in Z holds
( 1 + (sin . x) <> 0 & 1 - (sin . x) <> 0 ) ) holds
( tan + (cos ^) is_differentiable_on Z & ( for x being Real st x in Z holds
((tan + (cos ^)) `| Z) . x = 1 / (1 - (sin . x)) ) )