Ok so:
sin^3 - cos^3
------------------
sin^2 - cos^2
=
sin^2 -sin cos + cos^2
--------------------------
sin + cos
=
1+sin cos
----------------
sin + cos
EDIT: Sorry! I realised i factorised it wrong! But the book still says it's wrong! Don't worry though, I think the book is wrong, thanks for te enormous help!