Find the principal value of the following :\(\tan^{-1}\sqrt{3}-\cot^{

1.	Find the principal value of the following :\(\tan^{-1}\sqrt{3}-\cot^{-1}(-\sqrt{3})^3\)
Answer» \(\tan^{-1}\sqrt{3}-\cot^{-1}(-\sqrt{3})\) 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(\(\sqrt{3}\)) \(=\frac{\pi}{3}-\left(\pi-\frac{\pi}{6}\right)\) \(=\frac{\pi}{3}-\frac{5\pi}{6}\) \(=-\frac{3\pi}{6}=-\frac{\pi}{2}\)

Find the principal value of the following :\(\tan^{-1}\sqrt{3}-\cot^{-1}(-\sqrt{3})^3\)

Answer»

\(\tan^{-1}\sqrt{3}-\cot^{-1}(-\sqrt{3})\)

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(\(\sqrt{3}\))

\(=\frac{\pi}{3}-\left(\pi-\frac{\pi}{6}\right)\)

\(=\frac{\pi}{3}-\frac{5\pi}{6}\)

\(=-\frac{3\pi}{6}=-\frac{\pi}{2}\)