Question

The equation
${\tan }^{-1}x-co{t}^{-1}x={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)has$

• A. no solution
• B. unique solution
• C. infinite solutions
• D. two solutions

Answer 1

The correct option is B unique solution

We have
${\tan }^{-1}x-co{t}^{-1}x={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
and we know that${\tan }^{-1}x+co{t}^{-1}x=\frac{\pi }{2}$
Adding them, we get,
$2{\tan }^{-1}x=\frac{2\pi }{3}\Rightarrow {\tan }^{-1}x=\frac{\pi }{3}\Rightarrow x=\sqrt{3}.$
Therefore, the equation has a unique solution.