Evaluate the following: sec^-1{sec(-13π/4)}

Question

Evaluate the following:

sec^-1\(\{sec(-\frac{13π}4)\}\)

Answer 1

As sec(–θ) is sec(θ)

∴ sec\((\frac{-7\pi}3)\) = sec \((\frac{7\pi}3)\)

The value of sec \((\frac{-13\pi}4)\) is -√2.

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

and sec \((\frac{3\pi}4)\) = -√2.

Therefore, the value of sec^-1sec\((\frac{-13\pi}4)\)  is \(\frac{3\pi}4.\)