Solve the equations.`tan^(-1)(1-x)/(1+x)=1/2tan^(-1)x ,(x >0)`

1.	Solve the equations.`tan^(-1)(1-x)/(1+x)=1/2tan^(-1)x ,(x >0)`
Answer» `tan^(-1)""(1-x)/(1+x)=(1)/(2)tan^(-1)x, (x gt0)` `tan^(-1)1-tan^(-1)x=(1)/(2)tan^(-1)x` `implies (pi)/(4)=(1)/(2)tan^(-1)x+tan^(-1)x` `implies(3)/(2)tan^(-1)x=(pi)/(4)` `impliestan^(-1)x=(pi)/(4)` `implies tan^(-1)=(pi)/(6)` `implies x=tan""(pi)/(6)=(1)/(sqrt(3))`

Discussion

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