Question

Solve the following equation for x:

`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`

Answer 1

`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`

`=>cos^-1((1-x^2)/(1+x^2))+1/2xx2tan^-1x=(2x)/3`   `[becausetan^-1((2x)/(1-x^2))=2tan^-1x]`

`=>2tan^-1x+tan^-1x=(2x)/3`     `[becausecot^-1((1-x^2)/(1+x^2))=2tan^-1x]`

`=>3tan^-1x=(2x)/3`

`=>tan^-1x=(2x)/9`

`=>x=tan((2x)/9)`