Find the principal values of `sec^(-1)2/(sqrt(3))` and `sec^(-1)(-2)`

Explanation

Let `sec ^{-1}(frac{2}{sqrt{3}})=y`


`Rightarrow sec y=frac{2}{sqrt{3}}=sec (frac{pi}{6})`


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

Therefore, the principal value of `sec ^{-1}(frac{2}{sqrt{3}})` is `frac{pi}{6}`