Evaluate the following: cosec^-1(cosec 13π/6)

Question

Evaluate the following:

cosec^-1(cosec \(\frac{13\pi}6\))

Answer 1

The value of cosec\((\frac{13\pi}6)\) is 2.

∴ The question becomes cosec^–1(2)

Let, cosec^–1(2) = y

∴ cosec y = 2

⇒ cosec\((\frac{\pi}6)\) = 2

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

cosec\((\frac{\pi}6)\) = 2

Therefore, the value of cosec^-1(cosec\((\frac{13\pi}6)\)) is \(\frac{\pi}6.\)