Evaluate each of the following:
As we know cosec(–θ) = –cosecθ
∴ cosec = –cosec
–cosec can be written as –cosec
Also,
cosec(2π+θ) = cosecθ
∴ –cosec = –cosec
As we know –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.