Evaluate: $\sin^{-1} \left( \sin \frac{3\pi}{4} \right) + \cos^{-1}(\cos \pi) + \tan^{-1}(1)$.

$\frac{3\pi}{2}$

The correct answer is Option (2) → $\frac{3\pi}{2}$ ##

$\sin^{-1} \left( \sin \frac{3\pi}{4} \right) + \cos^{-1}(\cos \pi) + \tan^{-1}(1)$

$= \sin^{-1} \left( \sin \left( \pi - \frac{\pi}{4} \right) \right) + \cos^{-1}(\cos \pi) + \tan^{-1} \left( \tan \frac{\pi}{4} \right)$

$= \sin^{-1} \left( \sin \frac{\pi}{4} \right) + \cos^{-1}(\cos \pi) + \tan^{-1} \left( \tan \frac{\pi}{4} \right)$

$= \frac{\pi}{4} + \pi + \frac{\pi}{4} = \frac{3\pi}{2}$