Question

${\tan }^{-1}1+{\tan }^{-1}2+{\tan }^{-1}3$ is equal to

• A. $0$
• B. $\pi$
• C. $\frac{\pi }{2}$
• D. None of these

Answer 1

Answer: (B)

$\pi$

${\tan }^{-1}1+{\tan }^{-1}2+{\tan }^{-1}3$ is equal to:

using ${\tan }^{-1}x+{\tan }^{-1}y={\tan }^{-1}\left(\frac{x+y}{1-xy}\right),xy>1$

$={\tan }^{-1}1+{\tan }^{-1}3+{\tan }^{-1}2$

$=\frac{\pi }{4}+{\tan }^{-1}\left(\frac{2+3}{1-6}\right)$

$=\frac{\pi }{4}+{\tan }^{-1}-1$

$=\frac{\pi }{4}+\frac{3\pi }{4}$

$=\pi$