theorem :: FDIFF_10:32

for Z being open Subset of REAL st Z c= dom (sin (#) (sin - cos)) holds
( sin (#) (sin - cos) is_differentiable_on Z & ( for x being Real st x in Z holds
((sin (#) (sin - cos)) `| Z) . x = (((sin . x) ^2) + ((2 * (sin . x)) * (cos . x))) - ((cos . x) ^2) ) )