theorem Th6: :: INTEGR14:6

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