The value of $\tan^{-1}(1)+\cos^{-1}(-\frac{\sqrt{3}}{2}) + \sin^{-1} (\frac{1}{2})$ is
Answer & explanation
Correct answer: option 1
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 $=\frac{\pi}{4}+\frac{5\pi}{6}+\frac{\pi}{6}$
$=\frac{\pi}{4}+\frac{6\pi}{6}$
$=\frac{\pi}{4}+\pi$
$=\frac{5\pi}{4}$