Question

If 3 tan^-1x + cot^-1x = π, then x = ____________________.

Answer 1

$3{\tan }^{-1}x+{\cot }^{-1}x=\mathrm{\pi }$ (Given)

$\Rightarrow 2{\tan }^{-1}x+\frac{\mathrm{\pi }}{2}=\mathrm{\pi }\left({\tan }^{-1}x+{\cot }^{-1}x=\frac{\mathrm{\pi }}{2}\right)$

$\Rightarrow 2{\tan }^{-1}x=\mathrm{\pi }-\frac{\mathrm{\pi }}{2}=\frac{\mathrm{\pi }}{2}$

$\Rightarrow {\tan }^{-1}x=\frac{\mathrm{\pi }}{4}$

$\Rightarrow x=\tan \frac{\mathrm{\pi }}{4}=1$

Thus, the value of x is 1.

If 3tan⁻¹x + cot⁻¹x = $\mathrm{\pi }$, then x = ___1___.