Question:
Write.the principal value of $\tan ^{-1} 1+\cos ^{-1}\left(-\frac{1}{2}\right)$
Solution:
$\tan ^{-1} 1+\cos ^{-1}\left(-\frac{1}{2}\right)=\tan ^{-1}\left(\tan \frac{\pi}{4}\right)+\cos ^{-1}\left(\cos \frac{2 \pi}{3}\right)$
$=\frac{\pi}{4}+\frac{2 \pi}{3}$
$=\frac{11 \pi}{12}$