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  4. The equation tan -1 x- cot -1 x= tan -1((1/√3)) has

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Q. The equation $\tan ^{-1} x-\cot ^{-1} x=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$ has

Solution:

Let $\tan ^{-1} x-\cot ^{-1} x=\frac{\pi}{6}$
W.K.T $\tan ^{-1} x+\cot ^{-1} x=\frac{\pi}{2}$
$2 \tan ^{-1} x=\frac{2 \pi}{3}$
$\tan ^{-1} x=\pi / 3$
$x=\sqrt{3}$
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