## Trigonometry 7th Edition

$\frac{\cos^{2}\theta}{\sin\theta}$ or $\cot\theta\cos\theta$
Given expression is- $\frac{1}{\sin\theta} - \sin\theta$ = $\frac{1}{\sin\theta} - \sin\theta\times\frac{\sin\theta}{\sin\theta}$ = $\frac{1}{\sin\theta} -\frac{\sin^{2}\theta}{\sin\theta}$ = $\frac{1 - \sin^{2}\theta}{\sin\theta}$ = $\frac{\cos^{2}\theta}{\sin\theta}$ (Recall first Pythagorean identity) = $\frac{\cos\theta}{\sin\theta}. \cos\theta$ =$\cot\theta\cos\theta$