Question

The solution of $ta{n}^{-1}x+2co{t}^{-1}x=\frac{2\pi }{3}$ is

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is D

$ta{n}^{-1}x+2co{t}^{-1}x=\frac{2\pi }{3}$
$\Rightarrow \frac{\pi }{2}+co{t}^{-1}x=\frac{2\pi }{3}$
$\Rightarrow co{t}^{-1}x=\frac{\pi }{6}$
$\therefore x=cot\frac{\pi }{6}$
$\Rightarrow x=\sqrt{3}$