theorem Th5: :: FDIFF_10:5

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)) ) )