Ans (B) 1
Given: \(3tan^{-1}x+4cot^{-1}x=2\pi \)
We can write the given equation as
\(3tan^{-1}x+3cot^{-1}x+cot^{-1}x=2\pi \)
\( \Rightarrow\:3(tan^{-1}x+cot^{-1}x)+cot^{-1}x=2\pi\)
\( \Rightarrow 3(\large\frac{\pi}{2})\)\(+cot^{-1}x=2\pi \)
\( \Rightarrow cot^{-1}x=2\pi-3\large\frac{\pi}{2}=\frac{\pi}{2}\)
\(\Rightarrow x = 0\)