Answer
$$\cot \theta \cos \theta $$
Work Step by Step
$$\eqalign{
& \csc \theta - \sin \theta \cr
& {\text{Rewritting the expression csc}}\theta {\text{ in terms of sine}} \cr
& \frac{1}{{\sin \theta }} - \sin \theta \cr
& {\text{Simplifying}} \cr
& \frac{{1 - {{\sin }^2}\theta }}{{\sin \theta }} \cr
& {\text{Use the pythagorean identity }}1 - {\sin ^2}\theta = {\cos ^2}\theta \cr
& \frac{{{{\cos }^2}\theta }}{{\sin \theta }} \cr
& {\text{Distribute}} \cr
& \left( {\frac{{\cos \theta }}{{\sin \theta }}} \right)\cos \theta \cr
& \cot \theta \cos \theta \cr} $$
