# How do you prove cos^-1(-x)+cos^-1x=pi?

Nov 26, 2016

#### Explanation:

Let $\cos A = x$ then $\cos \left(\pi - A\right) = - \cos A = - x$

Hence ${\cos}^{- 1} x = A$

and ${\cos}^{- 1} \left(- x\right) = \pi - A$

${\cos}^{- 1} \left(- x\right) + {\cos}^{- 1} x = \pi - A + A = \pi$