The value of $\cos^{-1} \left( \cos \frac{3\pi}{2} \right)$ is

$\frac{\pi}{2}$

The correct answer is Option (1) → $\frac{\pi}{2}$ ##

We have, $\cos^{-1} \left( \cos \frac{3\pi}{2} \right) = \cos^{-1} \left[ \cos \left( 2\pi - \frac{\pi}{2} \right) \right]$

$= \cos^{-1} \left( \cos \frac{\pi}{2} \right) \quad \left[ ∵\cos \left( 2\pi - \frac{\pi}{2} \right) = \cos \frac{\pi}{2} \right]$

$= \frac{\pi}{2} \quad \{ ∵\cos^{-1}(\cos x) = x, x \in [0, \pi] \}$