Question

The number of solution of the equation $2{\tan }^{-1}x+{\cot }^{-1}x=\frac{7\pi }{6}$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (A)

$2{\tan }^{-1}x+{\cot }^{-1}x=\frac{7\pi }{6}\Rightarrow {\tan }^{-1}x+\frac{\pi }{2}=\frac{7\pi }{6}\Rightarrow {\tan }^{-1}x=\frac{2\pi }{3}$
$\Rightarrow {\tan }^{-1}x\in \left(\frac{-\pi }{2},\frac{\pi }{2}\right)(x\in \varphi )$