Question

The value of tan `π/8` is ______.

Options

• `sqrt(3) - 1`

• `sqrt(2) + 1`

• `sqrt(2) - 1`

• `sqrt(3) + 1`

Answer 1

The value of tan `π/8` is `underlinebb(sqrt(2) - 1)`.

Explanation:

Let x = `π/8`

∴ 2x = `π/4`

We have, tan 2x = `(2 tan x)/(1 - tan^2x)`

∴ `tan  π/4 = (2 tan  π/8)/(1 - tan^2  π/8)`

Let y = `tan  π/8`

∴ 1 = `(2y)/(1 - y^2)`

∴ 1 – y² = 2y

∴ y² + 2y – 1 = 0

∴ y = `(-2 + 2sqrt(2))/2`

= `-1 ± sqrt(2)`

Since, `π/8` lies in I quadrant y = `tan  π/4` positive

∴ `tan  π/8 = sqrt(2) - 1`