Solve for `x :tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,x >0`

Answer

`x=frac{1}{sqrt{3}} `

Explanation

\begin{aligned}
&\tan ^{-1} (\frac{1-x}{1+x})=\frac{1}{2} \tan ^{-1} x \\
&\Rightarrow \tan ^{-1} 1-\tan ^{-1} x=\frac{1}{2} \tan ^{-1} x \\
&\Rightarrow \frac{\pi}{4}=\frac{3}{2} \tan ^{-1} x \\
&\Rightarrow \tan -1 x=\frac{\pi}{6} \\
&\Rightarrow x=\tan \frac{\pi}{6} \\
&\therefore x=\frac{1}{\sqrt{3}}
\end{aligned}