Question

Find the principal value of the following:

`sec^(-1) (2/sqrt(3))`

Answer 1

Let `sec^(-1) (2/sqrt(3)) = y`.

Then, `sec y = 2/sqrt(3) = sec (pi/6)`.

We know that the range of the principal value branch of sec⁻¹ is `[0, pi] - {pi/2}` and `sec (pi/6) = 2/sqrt(3)`.

Therefore, the principal value of `sec^(-1) (2/sqrt(3))` is `pi/6`.