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If \tan ^{-1} y=4 \tan ^{-1} x, then \frac{1}{y} is zero for
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If \tan ^{-1} y=4 \tan ^{-1} x, then \frac{1}{y} is zero for

If we put x=\tan \theta, the given equality becomes \tan ^{-1} y=4 \theta

    \[\begin{array}{l} \Rightarrow y=\tan 4 \theta=\frac{2 \tan 2 \theta}{1-\tan ^{2} 2 \theta}=\frac{2\left[\frac{2 \tan \theta}{1-\tan ^{2} \theta}\right]}{1-\left(\frac{2 \tan \theta}{1-\tan ^{2} \theta}\right)^{2}} \\ =\frac{2 \times 2 x\left(1-x^{2}\right)}{\left(1-x^{2}\right)^{2}-4 x^{2}}=\frac{4 x\left(1-x^{2}\right)}{1-6 x^{2}+x^{4}} \end{array}\]

\therefore \frac{1}{y} is zero if x^{4}-6 x^{2}+1=0

    \[\Rightarrow x^{2}=\frac{6 \pm \sqrt{36-4}}{2}=3 \pm 2 \sqrt{2}=(1 \pm \sqrt{2})^{2}\]

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