Question

The principal value of `[tan^-1sqrt(3) - cot^-1(-sqrt(3))]` is ______.

Options

• π

• `-π/2`

• 0

• `2sqrt(3)`

Answer 1

The principal value of `[tan^-1sqrt(3) - cot^-1(-sqrt(3))]` is `underlinebb(-π/2)`.

Explanation:

We have,

 `tan^-1sqrt(3) - cot^-1(-sqrt(3))`

= `π/3 - (π - π/6)`

= `tan^-1(tan  π/3) - π + cot^-1 cot  π/6`

= `π/3 - (5π)/6`

= `-π/2`