$\cos^{-1}\left(\cos\frac{7\pi}{6}\right)$ equals:

$\frac{5\pi}{6}$

The correct answer is Option (2) → $\frac{5\pi}{6}$

\[ \cos^{-1}\left(\cos \frac{7\pi}{6}\right) \]

Since \(\frac{7\pi}{6} > \pi\), it lies outside the principal range of \(\cos^{-1}x\), which is \([0, \pi]\). The equivalent angle in this range having the same cosine value is: \[ \cos^{-1}\left(\cos \frac{7\pi}{6}\right) = \pi - \left(\frac{7\pi}{6} - \pi\right) = \pi - \frac{\pi}{6} = \frac{5\pi}{6} \]