theorem :: DIFF_3:78

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