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/sqrt3= sec y(pi/6)`

We know that the range of the principal value branch of sec⁻¹ is `[0,pi] - {pi/2}`.

Then `sec (pi/6) = 2/sqrt3`

Therefore, the principal value of `sec^(-1) (2/sqrt3)` is `pi/6`.