Question

For the inverse trigonometric functions, which of the following Principal Value Branch is not correctly defined?

Options

• tan⁻¹: R → `[(π/2, π/2)]`

• Sec⁻¹: R − (−1, 1) → [0, π] − `[π/2]`

• Cot⁻¹: R → (0, π)

• cosec⁻¹: R − (−1, 1) → `[−π/2,π/2]`

Answer 1

cosec⁻¹: R − (−1, 1) → `[−π/2,π/2]`

Explanation:

The Principal Value Branch for cosec⁻¹x is defined as the interval where the sine function is one-to-one, except the point where the function is undefined.

Cosec(x) = `1/sin(x)`

At x = 0, sin (0) = 0, which makes cosec(0) undefined.

Therefore, the value 0 must be removed from the range.