Establish each identity.

$\displaystyle cos(2x)/1 + sin(2x) = cotx - 1/ cotx + 1$

Now in the solutions manual, this is what they have in the middle:

$\displaystyle (cosx- sinx)(cosx+sinx)/cos^2x + sin^2x + 2sinxcosx$ =

$\displaystyle (cosx- sinx)(cosx+sinx)/(cosx+sinx)(cosx+sinx)$

How did they get rid of $\displaystyle 2sinxcosx$?

Thanks.