Question

(2) tan-11* tan 1x x>0 1+x

JEE/Engineering Exams

Maths

Solution

163

4.0 (1 ratings)

( tan ^{-1}left(frac{1-x}{1+x}right)=frac{1}{2} tan ^{-1} x ) If ( 2 tan ^{-1}left(frac{1-x}{1+x}right)=tan ^{-1} x ) ( left.=^{prime} 2 tan ^{-1} x=tan ^{-1} frac{2 x}{1-x^{2}}right] ) ( =tan ^{-1}left[begin{array}{c}2left(frac{1-x}{1+x}right) 1-left(frac{1-x}{1+x}right)^{2}end{array}right]=tan ^{-1} x ) if ( frac{2(1-x)}{frac{1+x}{(1+x)^{2}-(1-x)^{2}}}=x cdot ) ( frac{1+x y^{7}}{(1+x)^{2}} ) ( Rightarrow frac{2(1-x)(1+x)}{x+x^{2}+2 x-1-x^{2}+2 x}=x ) ( Rightarrow quad frac{2left(1-x^{2}right)}{244 x}= ) ( begin{aligned} 2 x^{2}+3 x^{2} &=2 x^{2} end{aligned} ) ( y=x^{2}=1 / 3 ) ( x>0 ) ( overrightarrow{S O}_{9}=frac{x}{B}=frac{pm 1}{1 / 3} / sqrt{3} cdot B u t )