Perform each indicated operation (using sin θ and cos θ) and simplify the result.
(cosθ / sinθ) + (sinθ / 1+cosθ)=?
$\displaystyle \frac{\cos \theta}{\sin \theta}+\frac{\sin \theta}{1+ \cos \theta}=\frac{\cos^2 \theta + \sin^2 \theta + \cos \theta}{\sin \theta (1+ \cos \theta)}$
$\displaystyle =\frac{1+\cos \theta}{\sin \theta (1+ \cos \theta)}=\frac{1}{\sin \theta}.$