Question

Find the principal value of sec⁻¹(2/√3).

Answer 1

Let sec⁻¹(2/√3)=y, then sec=2/√3=(π/6)
We know that the range of the principal value branch of sec⁻¹ is [0,π​]−{π/2}  and (π/6)=2/√3.
Therefore, the principal value of sec⁻¹(2/√3) is π/6.