Question

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

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

Answer 1

Answer: (B)

Let ${\tan }^{-1}x-{\cot }^{-1}x=\frac{\pi }{6}$
W.K.T ${\tan }^{-1}x+{\cot }^{-1}x=\frac{\pi }{2}$
$2{\tan }^{-1}x=\frac{2\pi }{3}$
${\tan }^{-1}x=\pi /3$
$x=\sqrt{3}$
Unique solution