theorem :: FDIFF_9:21

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))) ) )