theorem :: DIFF_3:86

for h, x being Real
for f being Function of REAL,REAL st ( for x being Real holds f . x = (cot (#) cos) . x ) & x in dom cot & x + h in dom cot holds
(fD (f,h)) . x = (((1 / (sin (x + h))) - (sin (x + h))) - (1 / (sin x))) + (sin x)