I used LaTeX, you can click the image to see how I done it - you can find out more here:
http://www.mathhelpforum.com/math-help/latex-help/
I'm not sure how to try it, I've done the difference of two squares but that only gives $\displaystyle \frac{(1-\cos \theta)(1+\cos \theta)}{1+\sin \theta}$
Using the Pythagorean identity gives only $\displaystyle \frac{\sin^2 \theta}{1+\sin \theta}$
Edit: this doesn't appear to be an identity - counterexample $\displaystyle \theta = \frac{\pi}{4}$
$\displaystyle \frac{1-cos^2 \left(\frac{\pi}{4}\right)}{1+\sin \left(\frac{\pi}{4}\right)} = \frac{1-\frac{1}{2}}{1+\frac{\sqrt2}{2}} = \frac{\frac{1}{2}}{\frac{2+\sqrt2}{2}} = \frac{1}{2+\sqrt2} = \frac{2-\sqrt2}{2} $
$\displaystyle \sin \left(\frac{\pi}{4}\right) = \frac{\sqrt2}{2} \neq \frac{2-\sqrt2}{2} $