Answer
$\cot^{2}\theta$
Work Step by Step
Given expression is-
$\frac{\cot\theta}{\tan\theta}$
= $\frac{\cos\theta/\sin\theta}{\sin\theta/\cos\theta}$
= $ \frac{\cos\theta}{\sin\theta} \times \frac{\cos\theta}{\sin\theta}$
= $\frac{\cos^{2}\theta}{\sin^{2}\theta}$
= $\cot^{2}\theta$
Alternate Method-
$\frac{\cot\theta}{\tan\theta}$ = $\cot\theta\times\frac{1}{\tan\theta}$
= $\cot\theta\times\cot\theta$
= $\cot^{2}\theta$
