Solve `tan^(-1) x + sin^(-1) x = tan^(-1) 2x`

Explanation

`tan^(-1) x + sin^(-1) x = tan^(-1) 2x`
`rArr sin^(-1) x = tan^(-1) 2x - tan^(-1) x`
`rArr tan^(-1).(x)/(sqrt(1 - x^(2))) = tan^(-1) [(2 x - x)/(1 + 2x^(2))]`
`rArr (x)/(sqrt(1 - x^(2))) = (x)/(1 + 2x^(2))`
`rArr 2x^(3) + x = x sqrt(1 - x^(2))`
`rArr 2x^(3) - x sqrt(1 - x^(2)) + x = 0`
`rArr x(2x^(2) - sqrt(1 - x^(2)) + 1) = 0`
`rArr x = 0 " or " 2x^(2) + 1 = sqrt(1 - x^(2))`
`rArr x = 0 " or " 4x^(4) + 4x^(2) + 1 = 1 - x^(2)`
`rArr x = 0 " or " 4x^(4) + 5x^(2) = 0`
`rArr x = 0` is the only solution