Let $\mathit{c}\mathit{o}{\mathit{s}}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ = x
⇒ cos x = - $\frac{\sqrt{3}}{2}$
⇒ cos x = - cos $\left(\frac{\mathit{\pi }}{6}\right)$
⇒ cos x = cos $\left(\mathit{\pi }-\frac{\mathit{\pi }}{6}\right)$
⇒ cos x = cos $\left(\frac{5\mathit{\pi }}{6}\right)$
⇒ x = $\frac{5\mathit{\pi }}{6}$
Therefore, the principal value of $\mathit{c}\mathit{o}{\mathit{s}}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ is $\frac{5\mathit{\pi }}{6}$