Find the principal values of each of the following:

Question

Philoid · Accepted Answer

cosec^–1(2cos)

Let us assume 2cos = θ

We know cos =

∴ 2cos = 2

⇒ 2cos = –1

∴ The question converts to cosec^–1(–1)

Now,

cosec^–1–1 ⁼ y

⇒ cosec y = –1

⇒ –cosec y = 1

⇒ –cosec = 1

As we know cosec(–θ) = –cosecθ

∴ –cosec = cosec

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

cosec = –1

Therefore, the principal value of cosec^–1(2cos) is.