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If \( 3 \tan ^{-1} x+\cot ^{-1}=\Pi \) then \( x \) equal to
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\( 11 \)
Given that, $3 \tan ^{-1} x+\cot ^{-1} x=\pi$
$\Rightarrow 2 \tan ^{-1} x+\left(\tan ^{-1} x+\cot ^{-1} x\right)=\Pi$
Since, $\tan ^{-1} x+\cot ^{-1} x=\frac{\Pi}{2} .$ Then
$\Rightarrow 2 \tan ^{-1} x+\frac{\Pi}{2}=\pi$
$\Rightarrow 2 \tan ^{-1} x=\frac{\Pi}{2}$
$\Rightarrow \tan ^{-1} x=\frac{\Pi}{4}$
$\Rightarrow x=\tan \frac{\Pi}{4}=1$
$\Rightarrow 2 \tan ^{-1} x+\left(\tan ^{-1} x+\cot ^{-1} x\right)=\Pi$
Since, $\tan ^{-1} x+\cot ^{-1} x=\frac{\Pi}{2} .$ Then
$\Rightarrow 2 \tan ^{-1} x+\frac{\Pi}{2}=\pi$
$\Rightarrow 2 \tan ^{-1} x=\frac{\Pi}{2}$
$\Rightarrow \tan ^{-1} x=\frac{\Pi}{4}$
$\Rightarrow x=\tan \frac{\Pi}{4}=1$
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