#### Answer

$-\cos^{2}\theta\cdot\csc\theta$

#### Work Step by Step

$\cot(-\theta)=-\cot\theta \quad \sec(-\theta)=\sec\theta .$
$\displaystyle \cot\theta=\frac{\cos\theta}{\sin\theta}, \displaystyle \quad \sec\theta=\frac{1}{\cos\theta}\quad \csc\theta=\frac{1}{\sin\theta}$
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$\displaystyle \frac{\cot(-\theta)}{\sec(-\theta)}=\frac{-\cot\theta}{\sec\theta}=-\cot\theta\times\frac{1}{\sec\theta}$
$=-\displaystyle \frac{\cos\theta}{\sin\theta}\times\frac{1}{\sec\theta}$
$=-\displaystyle \frac{\cos\theta}{\sin\theta}\times\cos\theta$
$=-\displaystyle \cos^{2}\theta\times\frac{1}{\sin\theta}$
$=-\cos^{2}\theta\cdot\csc\theta$