Question

What is the principal value of cos^-1(1/root2).

cos^-1 \(\frac{1}{\sqrt{2}}\)

Answer 1

cos^-1 \(\frac{1}{\sqrt{2}}\) = co^-1 (cos \(\frac{\pi}{4}\)) = \(\frac{\pi}{4}\)

∴ Principal value branch of cos^-1 x is

∴ Principal value of cos-1 \(\frac{1}{\sqrt{2}}\) is \(\frac{\pi}{4}\).