\(\tan^{-1}\sqrt{3}-\cot^{-1}(-\sqrt{3})\)
Putting the value of tan -1\(\sqrt{3}\) and using formula
\(\cot^{-1}(-\mathrm x)= \pi-\cot^{-1}\mathrm x\)
\(=\frac{\pi}{3}-(\pi-\cot^{-1}(\sqrt{3}))\)
Putting the value of cot -1(\(\sqrt{3}\))
\(=\frac{\pi}{3}-\left(\pi-\frac{\pi}{6}\right)\)
\(=\frac{\pi}{3}-\frac{5\pi}{6}\)
\(=-\frac{3\pi}{6}=-\frac{\pi}{2}\)
