Prove that : \[\frac{\tan \theta-\cot \theta}{\sin \theta \cos \theta}=\sec ^{2} \theta-\operatorname{cosec}^{2} \theta \]

\[\begin{aligned} \mathrm{LHS}=\frac{\tan \theta-\cot \theta}{\sin \theta \cos \theta}= & \frac{\dfrac{\sin \theta}{\cos \theta}-\dfrac{\cos \theta}{\sin \theta}}{\sin \theta \cos \theta} \\ & =\frac{\sin ^{2} \theta-\cos ^{2} \theta}{\sin ^{2} \theta \cos ^{2} \theta} \\ & =\frac{1}{\cos ^{2} \theta}-\frac{1}{\sin ^{2} \theta} \\ & =\sec ^{2} \theta-\operatorname{cosec}^{2} \theta=\mathrm{RHS} \end{aligned} \]