Question

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

• A. $0$
• B. $1$
• C. $-1$
• D. $\frac{1}{2}$

Answer 1

The correct option is B $1$

$3{\tan }^{-1}x+{\cot }^{-1}x=\pi$
$3{\tan }^{-1}x+\frac{\pi }{2}-{\tan }^{-1}x=\pi$
$2{\tan }^{-1}x=\frac{\pi }{2}$
${\tan }^{-1}x=\frac{\pi }{4}$
$\Rightarrow x=1$