# How do you simplify cottheta/costheta?

Dec 19, 2016

$\cot \frac{\theta}{\cos} \theta = \csc \theta$

#### Explanation:

$\cot \frac{\theta}{\cos} \theta = \frac{1}{\tan} \theta \cdot \frac{1}{\cos} \theta$

$= \cos \frac{\theta}{\sin} \theta \cdot \frac{1}{\cos} \theta$

$= \cancel{\cos} \frac{\theta}{\sin} \theta \cdot \frac{1}{\cancel{\cos}} \theta = \frac{1}{\sin} \theta$

$= \csc \theta$

Dec 19, 2016

$\csc \left(\theta\right)$

#### Explanation:

We have: $\frac{\cot \left(\theta\right)}{\cos \left(\theta\right)}$

First, let's apply the standard trigonometric identity $\cot \left(\theta\right) = \frac{\cos \left(\theta\right)}{\sin \left(\theta\right)}$:

$= \frac{\frac{\cos \left(\theta\right)}{\sin \left(\theta\right)}}{\cos \left(\theta\right)}$

$= \frac{\cos \left(\theta\right)}{\sin \left(\theta\right) \cos \left(\theta\right)}$

$= \frac{1}{\sin \left(\theta\right)}$

Then, let's apply the identity $\csc \left(\theta\right) = \frac{1}{\sin \left(\theta\right)}$

$= \csc \left(\theta\right)$