I couldn't find example you're talking about. Can you provide number of example, page and your book's edition number?
Also, in Chapter 1, Cos(a+b) = cos a * cos b - (not +) sin a *sin b.
Yes this is a typo. But you've written it correctly here.
cos(a+b) = cosa*cosb -
cos(a-b) = cosa*cosb +
These are correct, while in the book signs in both eq. for cosine are opposite.
Btw. in some
(I have really seen it) books (3 ed.) there is one more typo on the same page a little bit above.
sin(-a) = -sin(a)
cos(-a) = cos(a).