# How do you find the exact value of cos(tan^-1(sqrt3/4))?

Nov 28, 2016

$\frac{4}{\sqrt{19}}$

#### Explanation:

Let $a = {\tan}^{- 1} \left(\frac{\sqrt{3}}{4}\right) \in {Q}_{1}$, wherein cosine is positive.

The given expression is

$\cos a = \frac{4}{\sqrt{{\left(\sqrt{3}\right)}^{2} + {4}^{2}}} = \frac{4}{\sqrt{19}}$,

using definitions

tan a = (opposite side)/ (adjacent side) and