Evaluate the following: sec^-1(sec 25π/6)

Question

Evaluate the following:

sec^-1sec \((\frac{25\pi}6)\)

Answer 1

sec \((\frac {25\pi} 6)\) = \((\frac 2{\sqrt3})\)

∴ The question converts to sec^-1\((\frac 2{\sqrt3})\)

Now,

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

and sec \((\frac{\pi}3)\) = \((\frac{2}{\sqrt3})\)

Therefore, the value of sec^-1sec\((\frac{25\pi}6)\) is \(\frac{\pi}3.\)