Find the value of x which satisfy equation `2 tan^(-1) 2x = sin^(-1).(

1.	Find the value of x which satisfy equation `2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))`
Answer» Correct Answer - `-(1)/(2) le x le (1)/(2)` `2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2)) = sin^(-1).(2(2x))/(1 + (2x)^(2))` `rArr -(pi)/(2) le 2 tan^(-1) 2x le (pi)/(2)` `rArr -(pi)/(4) le tan^(-1) 2x le (pi)/(4)` `rArr -1 le 2x le 1` `rArr -(1)/(2) le x le (1)/(2)`

Discussion

`tan^(-1)[(cosx)/(1+sinx)]`is equal to`pi/4-x/2,forx in (-pi/2,(3pi)/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-pi/2,pi/2)``pi/4-x/2,forx in (-(3pi)/2,pi/2)`
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