The value of $\tan^{-1}(1)+\cos^{-1}(-\frac{\sqrt{3}}{2}) + \sin^{-1} (\frac{1}{2})$ is

$\frac{5\pi}{4}$

The correct answer is Option (1) → $\frac{5\pi}{4}$

$\tan^{-1}(1)=\frac{\pi}{4}$

$\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)=\frac{5\pi}{6}$

$\sin^{-1}\left(\frac{1}{2}\right)=\frac{\pi}{6}$

Sum $=\frac{\pi}{4}+\frac{5\pi}{6}+\frac{\pi}{6}$

$=\frac{\pi}{4}+\frac{6\pi}{6}$

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

$=\frac{5\pi}{4}$