Write the following function in the simplest form: `tan^(-1)((3a^2x-x^3)/(a^3-3a x^2)), a >0;(-a)/(sqrt(3))lt=xlt=a/(sqrt(3))`

Explanation

`tan^(-1)((3a^(2)x-x^(3))/(a^(3)-3ax^(2)))`
`tan^(-1)((3a^(2)*a tan theta-a^(3)tan^(3)theta)/(a^(3)-3a*a^(2)tan^(2)theta))`
`=tan^(-1)((3 tan theta-tan^(3)theta)/(1-3 tan^(2)theta))" " Let x = a tan theta implies (x)/(a)=tan thetaimplies theta = tan^(-1)""((x)/(a))`
`=tan^(-1)(tan 3 theta)3 theta`
`3 tan^(-1)""(x)/(a)`