Evaluate the following: sec^-1(sec 5π/4)

Question

Evaluate the following:

sec^-1(sec \(\frac{5\pi}4\))

Answer 1

The value of sec\((\frac{5\pi}4)\) is -√2.

∴ The question becomes sec^–1(–√2).

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

and sec\((\frac{3\pi}4)\) = -√2

∴ The principal value of sec^–1(–√2) is \(\frac{3\pi}4.\)