Answer
$csc\theta \cos ^{2}\theta +\sin \theta =csc\theta $
Work Step by Step
$csc\theta \cos ^{2}\theta +\sin \theta =\dfrac {\cos ^{2}\theta }{\sin \theta }+\sin \theta =\dfrac {\cos ^{2}\theta +\sin ^{2}\theta }{\sin \theta }=\dfrac {1}{\sin \theta }=csc\theta $
