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

11th - 12th Class
Maths
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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}} )
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