# How do you evaluate tan^-1(tan(-(pi)/10))?

Feb 25, 2018

A fundamental property of all inverses is:

${f}^{-} 1 \left(f \left(x\right)\right) = x$

#### Explanation:

Applying the above property:

${\tan}^{-} 1 \left(\tan \left(x\right)\right) = x$

Substitute $x = - \frac{\pi}{10}$:

${\tan}^{-} 1 \left(\tan \left(- \frac{\pi}{10}\right)\right) = - \frac{\pi}{10}$