Question

The principal value of `tan^-1(tan  (9π)/8)` is ______.

Options

• `π/8`

• `(3π)/8`

• `- π/8`

• `- (3π)/8`

Answer 1

The principal value of `tan^-1(tan  (9π)/8)` is `underlinebb(π/8)`.

Explanation:

`tan^-1(tan  (9π)/8) = tan^-1(tan(π + π/8))`

= `tan^-1(tan  π/8)`  ...`[∵ π/8 ∈ ((-π)/2, π/2)]`

= `π/8`