# Simplify (cscxcosx)/(tanx+cotx)?

May 2, 2016

#### Explanation:

$\frac{\csc x \cos x}{\tan x + \cot x}$

= $\frac{\csc x \cos x}{\sin \frac{x}{\cos} x + \cos \frac{x}{\sin} x}$

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

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

= $\csc x \cos x \times \cos x \sin x$

= ${\cos}^{2} x \times \csc x \sin x$

= ${\cos}^{2} x \times 1 = {\cos}^{2} x$