Question

We have
[
begin{array}{l}
tan ^{-1}left(frac{1-x}{1+x}right)=frac{1}{2} tan ^{-1} x,(x>0)
Rightarrow tan ^{-1} 1-tan ^{-1} x=frac{1}{2} tan ^{-1} x
Rightarrow frac{3}{2} tan ^{-1} x=tan ^{-1} 1=frac{pi}{4}
Rightarrow tan ^{-1} x=left(frac{pi}{4} times frac{2}{3}right)=frac{pi}{6} Rightarrow x=tan left(frac{pi}{6}right)=frac{1}{sqrt{3}}
end{array}
]
Hence, ( x=frac{1}{sqrt{3}} )

# 1- X EXAMPLE 24 Solve tan-(1 = * = tan + x, (x>0). (CBSE 2008C, '11, *14c] EXAMPLE 24 Solve tan ICBSE 2 1 + x

Solution