Find the principal value of each of the following: `cos^(-1)(-(sqrt(3))/2)` (ii) `cos^(-1)(-1/(sqrt(2)))`

Explanation

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


Then `cos y=frac{sqrt{3}}{2}=cos (frac{pi}{6})`


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


Therefore the principle value of `cos ^{-1}(frac{sqrt{3}}{2})` is `frac{pi}{6}`