Question

If tan⁻¹ x = 3y, then ______.

Options

• `-π/2 < y < π/2`

• `-(3π)/2 < y < (3π)/2`

• `-π/6 < y < π/6`

• `-π/6 ≤ y ≤ π/6`

Answer 1

If tan⁻¹ x = 3y, then `underline bb(-π/6 < y < π/6)`.

Explanation:

tan⁻¹ x has a principal value range,

`-π/2 < tan^-1x < π/2`

So, 3y lies in this open interval. Dividing by 3:

∴ `-π/6 < y < π/6`