What follows is a last-minute addendum to Section 2.2.2, as this book goes to press.
Trig is an option for the algebraic transformation functions (introduced in Section 2.2.1) except
Trig -> True, these functions attempt to transform trigonometric functions in algebraic manipulations; with
Trig -> False, they leave the trigonometric functions unchanged.
Trig -> False is the default for these functions except
FullSimplify whose default is
Trig -> True. For example,
Apart leaves 2(cos(α) – cos(β)) csc(α) csc(β) unaltered:
In:= Apart[2 (Cos[α]- Cos[β]) Csc[α] Csc[β]] Out= 2 (Cos[α]- Cos[β]) Csc[α] Csc[β]]
Trig -> True, Apart rewrites the trigonometric expression: ...