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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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