Listen NCERT Audio Books to boost your productivity and retention power by 2X.
Find the principal values of each of the following:
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
.