# How do you find the value of cos (tan^-1 (2/3))?

$\pm \frac{3}{\sqrt{13}}$
Let $a = {\tan}^{- 1} \left(\frac{2}{3}\right)$.
As tan a = 2/3, cos a and sin a should both have the same sign and $a = {\tan}^{- 1} \left(\frac{2}{3}\right) = {33.7}^{o} \mathmr{and} {213.7}^{o}$, in $\left[0 , 2 \pi\right]$.
So, I take a as either, and so, $\cos a = \cos \left({\tan}^{- 1} \left(\frac{2}{3}\right)\right) = \pm \frac{3}{\sqrt{13}}$.