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

Answer: (B)

Solution: We have $3{\tan }^{-1}x+{\cot }^{-1}x=\pi$
$\Rightarrow 2{\tan }^{-1}x+{\tan }^{-1}x+{\cot }^{-1}x=\pi$
$\Rightarrow 2{\tan }^{-1}x+\frac{\pi }{2}=\pi$
$\left[\because {\tan }^{-1}x+{\cot }^{-1}x=\frac{\pi }{2}\right]$
$\Rightarrow 2{\tan }^{-1}x=\pi -\frac{\pi }{2}$
$\Rightarrow 2{\tan }^{-1}x=\frac{\pi }{2}$
$\Rightarrow {\tan }^{-1}x=\frac{\pi }{4}$
$\Rightarrow x=\tan \frac{\pi }{4}$
$\therefore x=1$