# Simplify (cscx-sinx)/(sinxcscx)?

Feb 14, 2017

#### Explanation:

$\frac{\csc x - \sin x}{\sin x \csc x}$

= $\frac{\csc x - \sin x}{\sin x \times \frac{1}{\sin} x}$

= $\frac{\csc x - \sin x}{\cancel{\sin} x \times \frac{1}{\cancel{\sin}} x}$

= $\frac{\csc x - \sin x}{1}$

= $\csc x - \sin x$

= $\frac{1}{\sin} x - \sin x$

= $\frac{1 - {\sin}^{2} x}{\sin} x$

= ${\cos}^{2} \frac{x}{\sin} x$

= $\cot s \csc x$