1. Ok so:

sin^3$\displaystyle \theta$ - cos^3$\displaystyle \theta$
------------------
sin^2$\displaystyle \theta$ - cos^2$\displaystyle \theta$

=

sin^2$\displaystyle \theta$-sin$\displaystyle \theta$cos$\displaystyle \theta$ + cos^2$\displaystyle \theta$
--------------------------
sin$\displaystyle \theta$ + cos$\displaystyle \theta$

=

1+sin$\displaystyle \theta$cos$\displaystyle \theta$
----------------
sin$\displaystyle \theta$ + cos$\displaystyle \theta$

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!

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