Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 1 of Exercise 4.5
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1
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
.
