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