Find the principal values of each of the following: sec^-1(2sin 3π/2)

Question

Find the principal values of each of the following:

sec^-1(2sin \(\frac{3\pi}4\))

Answer 1

The range of principal value of sec^-1 is [0, π] - {\(\frac{\pi}2\)}

And sec \((\frac{\pi}4)\) = √2

\(\therefore\) The principal value of sec^-1(2sin\(\frac{3\pi}4\)) is \(\frac{\pi}4.\)