The value of cosec = –2.

Let,

cosec^–1–2 ⁼ y

⇒ cosec y = –2

⇒ –cosec y = 2

⇒ –cosec = 2

As we know cosec(–θ) = –cosecθ

∴ –cosec = cosec

The range of principal value of cosec^–1 is –{0} and

cosec = –2

Therefore, the value of cosec^–1(cosec) is .