Question

If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.

Answer 1

If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is `sqrt(3)`.

Explanation:

We have, `cos(tan^-1x + cot^-1 sqrt(3))` = 0

⇒ `tan^-1x + cot^-1  sqrt(3) = cos^-1 0`

⇒ `tan^-1x + cot^-1 sqrt(3) = pi/2`

⇒ `tan^-1x = pi/2 - cot^-1 sqrt(3)`

⇒ `tan^-1x = tan^-1 sqrt3)`  .....`(because tan^-1x + cot^-1x = pi/2)`

∴ x = `sqrt(3)`