cosec can be written as cosec

cosec = –cosec

Also,

–cosec(θ) = cosec(–θ)

⇒ –cosec = cosec

Now the question becomes cosec^–1(cosec)

cosec^–1(cosec x) = x

Provided x ϵ –{0}

∴ we can write cosec^–1(cosec.