Answer:
Option B
Explanation:
$\frac{tan^{-1})(\sqrt{3})-\sec^{-1}(-2)}{cosec^{-1}(-\sqrt{2})+\cos^{-1}(-\frac{1}{2})}$
= $\frac{tan^{-1}(\sqrt{3})-(\pi-\sec^{-1}(-2))}{-cosec^{-1}(\sqrt{2})+\pi -\cos^{-1}(\frac{1}{2})}$
= $\frac{\frac{\pi}{3}-\left(\pi-\frac{\pi}{3}\right)}{-\frac{\pi}{4}+\pi-\frac{\pi}{3}}=\frac{\frac{2 \pi}{3}-\pi}{\pi-\frac{\pi}{4}-\frac{\pi}{3}}$
= $\frac{-\frac{\pi}{3}}{\frac{12\pi-3\pi-4\pi}{12}}=\frac{-\frac{ \pi}{3}}{\frac{5\pi}{12}}=-\frac{4}{5}$
