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!