Question

Values of tan^–1 – sec^–1(–2) is equal to

Options

• 0

• `- pi/3`

• `- pi/3`

• `(2pi)/3`

Answer 1

`- pi/3`

Explanation:

Let `tan^-1 sqrt(3)` = x

⇒ `tan x = sqrt(3) = tan  pi/3`

Range of the principle value of tan^–1x is `(-pi/2, pi/2)`

∴ `tan^-1 sqrt(3) = pi/3`

Set `sec^-1 (-2) = y = sec y = - 2`

= `- sec (pi/3) = sec(pi - pi/3) = sec  (2pi)/3`

Range of the principal value of sec^–1x is `[0, |pi/2|` ∴ `sec^-1(-2) = (2pi)/3 pi]`

Thus, `tan^-1sec^-1(–2) = pi/3 - (2pi)/3 = - pi/3`