Question

Principal value of `"cosec"^(−1)((−2)/sqrt3)` is equal to ______.

Options

• `−π/3`

• `π/3`

• `π/2`

• `−π/2`

Answer 1

Principal value of `"cosec"^(−1)((−2)/sqrt3)` is equal to `bbunderline(−π/3)`.

Explanation:

Let `"cosec"^(−1)((−2)/sqrt3) = θ`

⇒ cosec = `−2/sqrt3 = − "cosec" π/3 = "cosec" ((−π)/3)`

⇒ θ = `(−π)/3 ∈ [−π/3, π/2] − {0}`

∴ Principal value of cosec⁻¹ `((−2)/sqrt3) "is" ((−π)/3)`