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

(D)
Let \(\sin ^{-1}\left(\frac{-1}{2}\right)=\alpha\), where \(\frac{-\pi}{2} \leq \alpha \leq \frac{\pi}{2}\)
\(\sin \alpha=\frac{-1}{2}=-\sin \frac{\pi}{6}=\sin \left(\frac{-\pi}{6}\right) \Rightarrow \alpha=-\pi / 6\)
Let \(\cos ^{-1}\left(\frac{-\sqrt{3}}{2}\right)=\beta\), where \(0 \leq \beta \leq \pi\)
\(\cos \beta=\frac{-\sqrt{3}}{2}=\frac{-\cos \pi}{6} \Rightarrow \cos \left(\pi-\frac{\pi}{6}\right)=\frac{\cos 5 \pi}{6} \Rightarrow \beta\) \(=\frac{5 \pi}{6}\)
\(\therefore \sin ^{-1}\left(\frac{-1}{2}\right)+\cos ^{-1}\left(\frac{-\sqrt{3}}{2}\right)=\frac{-\pi}{6}+\frac{5 \pi}{6} \quad=\frac{4 \pi}{6}\) \(=\frac{2 \pi}{3}=\) \(\cos ^{-1}\left(\frac{-1}{2}\right)\)