Question

if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc 

Answer 1

`tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`

`tan^(-1)b + tan^(-1) c = pi - tan^(-1) (a)`

`tan^(-1) ((b+c)/(1-bc)) = pi - tan^(-1) a`

`(b+c)/(1-bc) = tan(pi - tan^(-1) a)`

`(b + c)/(1-bc) = -tan(tan^(-1)a)`

`(b+c)/(1-bc) = -a`

b + c = -a + abc

`:. a + b + c = abc`