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