theorem Th6: :: FDIFF_10:6

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