Question

Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`

Answer 1

`tan^(-1) (sqrt3) -cot^(-1) (-sqrt3)`

`= tan^(-1) {tan (pi/3)} - cot^(-1) (cot (5pi)/6)`     [∵ Range of `tan^(-1) is (-pi/2, pi/2); pi/3 in (-pi/2, pi/2)`

and range of `cot^(-1) is [0, pi]; (5pi)/6 in [0,pi]]`

`= pi/3 - (5pi)/6`

`= -pi/2`