# How do you simplify cosxtanx+sinxcotx?

Mar 22, 2018

$\sin x + \cos x$

#### Explanation:

First, write everything in terms of sines and cosines.

$\left(\cos x\right) \left(\tan x\right) + \left(\sin x\right) \left(\cot x\right)$

$\left(\cos x\right) \left(\sin \frac{x}{\cos} x\right) + \left(\sin x\right) \left(\cos \frac{x}{\sin} x\right)$

$\frac{\cos x \cdot \sin x}{\cos} x + \frac{\sin x \cdot \cos x}{\sin} x$

Now, cancel out like terms in the numerator and denominator:

$\frac{\cancel{\cos} x \cdot \sin x}{\cancel{\cos}} x + \frac{\cancel{\sin} x \cdot \cos x}{\cancel{\sin}} x$

$\sin x + \cos x$

This is as simplified as the expression gets.