Question

${\tan }^{-1}\sqrt{3}-{\cot }^{-1}(-\sqrt{3})$ is equal to

• A. $\pi$
• B. $-\frac{\pi }{2}$
• C. $0$
• D. $2\sqrt{3}$

Answer 1

The correct option is B $-\frac{\pi }{2}$

${\tan }^{-}1\sqrt{3}=\frac{\pi }{3}$

and

${\cot }^{-}1(-\sqrt{3})=(\pi -\frac{\pi }{6})=\frac{5\pi }{6}$

$\therefore$ $\frac{\pi }{3}-\frac{5\pi }{6}=\frac{-3\pi }{6}=\frac{-\pi }{2}$