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 principal value of cosec^–1(–√2) is .