Answer
$\dfrac {csc\theta +\cot \theta }{\tan \theta +\sin \theta }=csc\theta \cot \theta $
Work Step by Step
$\dfrac {csc\theta +\cot \theta }{\tan \theta +\sin \theta }=\dfrac {\dfrac {1}{\sin \theta }\left( 1+\cos \theta \right) }{\dfrac {\sin \theta }{\cos \theta }\left( 1+\cos \theta \right) }=\dfrac {\cos \theta }{\sin ^{2}\theta }=csc\theta \cot \theta $
