Question

The principal value of `tan^{-1(sqrt3)}` is ______  

Options

• `pi/3`

• `(2pi)/3`

• `-pi/3`

• `(4pi)/3`

Answer 1

The principal value of `tan^{-1(sqrt3)}` is `underline(-pi/3)`.

Explanation:

Let `tan^{-1(sqrt3)}` = x

⇒ tan x = `-sqrt3`

⇒ `tanx = -tan(pi/3) = tan(-pi/3)`

The principal value branch of tan^-1x is `(-pi/2, pi/2)` and `-pi/2 < -pi/3<pi/2`.

⇒ `x = -pi/3`