Question

Find the principal value of sec-1$(\frac{2}{\sqrt3})$

Answer 1

Let sec-1$(\frac{2}{\sqrt3})=y$.
Then $sec \,y=\frac{2}{\sqrt3}=sec\bigg(\frac{\pi}{6}\bigg)$
We know that the range of the principal value branch of
sec-1 is $\bigg[0,\pi\bigg]-\frac{\pi}{2}and\, sec \,\frac{\pi}{6}=\frac {2}{\sqrt3}.$

Therefore, the principal value of sec-1$(\frac{2}{\sqrt3})$ is $\frac{\pi}{6}.$