Question

Find the principal value of `cot^-1 ((-1)/sqrt(3))`

Answer 1

Let y = `cot^-1 ((-1)/sqrt(3))`

Since, cot^–1(– x) = π – cot^–1x

∴ y = `π - cot^-1 (1/sqrt(3))`

⇒ y = `π - π/3`  ......`(∵ cot π/3 = 1/sqrt(3))`

⇒ y = `(2π)/3`

Since, range of cot^–1 is (0, π)

Hence, principal value is `(2π)/3`.