# How do you find the exact value of sec30cot45?

Jun 20, 2018

$\frac{2 \sqrt{3}}{3}$

#### Explanation:

$= \sec 30 \cot 45$

$= \frac{1}{\cos} 30 \cdot \frac{1}{\tan} 45$

use the unit circle to find exact values:

$\cos 30 = \frac{\sqrt{3}}{2}$

$\frac{1}{\cos} 30 = \frac{2}{\sqrt{3}}$

$\tan 45 = 1$

$\frac{1}{\tan} 45 = \frac{1}{1} = 1$

$= \sec 30 \cot 45 = \frac{2}{\sqrt{3}} \cdot 1 = \frac{2}{\sqrt{3}} = \frac{2 \sqrt{3}}{3}$