Question

Solve `3tan^(-1)x + cot^(-1) x = pi`

Answer 1

`3tan^(-1) x +  cot^(-1) x = pi`

`:. 2tan^(-1) x + tan^(-1) x + cot^(-1) = pi`

`:. 2tan^(-1) x + pi/2 = pi`

`2tan^(-1) x = pi = pi/2`

`tan^(-1) (x) = pi/2 - pi/4`

`x= tan (pi/2 - pi/4)`

x = 1