Question

If $3{\tan }^{-1}x+{\cot }^{-1}x=\pi$, then $x$ is equal to

• A. $0$
• B. $1$
• C. $-1$
• D. $1/2$

Answer 1

The correct option is B $1$

We have, $3{\tan }^{-1}x+{\cot }^{-1}x=\pi$

$\Rightarrow 2{\tan }^{-1}x+({\tan }^{-1}x+{\cot }^{-1}x)=\pi$

$\Rightarrow 2{\tan }^{-1}x+\frac{\pi }{2}=\pi$, $[\because {\tan }^{-1}x+{\cot }^{-1}x=\frac{\pi }{2}]$ is an identity

$\Rightarrow 2{\tan }^{-1}x=\pi -\frac{\pi }{2}=\frac{\pi }{2}$

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

$\therefore x=\tan \frac{\pi }{4}=1$