Question:
If $3 \tan ^{-1} x+\cot ^{-1} x=\pi$, then $x=$
Solution:
$3 \tan ^{-1} x+\cot ^{-1} x=\pi$ (Given)
$\Rightarrow 2 \tan ^{-1} x+\frac{\pi}{2}=\pi$
$\Rightarrow 2 \tan ^{-1} x=\pi-\frac{\pi}{2}=\frac{\pi}{2}$ $\left(\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}\right)$
$\Rightarrow \tan ^{-1} x=\frac{\pi}{4}$
$\Rightarrow x=\tan \frac{\pi}{4}=1$
If $3 \tan ^{-1} x+\cot ^{-1} x=\pi$, then $x=$ ___1___
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