Answer
$-\cot\theta$
Work Step by Step
$\displaystyle \tan\theta-\sec\theta\csc\theta=\frac{\sin\theta}{\cos\theta}-\frac{1}{\cos\theta}\times\frac{1}{\sin\theta}$
... common denominator: $\cos\theta\sin\theta$ ...
$=\displaystyle \frac{\sin^{2}\theta-1}{\cos\theta\sin\theta}$
$=\displaystyle \frac{-(1-\sin^{2}\theta)}{\cos\theta\sin\theta}$
$=\displaystyle \frac{-\cos^{2}\theta}{\cos\theta\sin\theta}$
$=-\displaystyle \frac{\cos\theta}{\sin\theta}$
$=-\cot\theta$
