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(–√2)
cosec–1 (–√2) =y
⇒ cosec y = –√2
⇒ –cosec y = √2
⇒ –cosec 
= √2
As we know cosec(–θ) = –cosecθ
∴ –cosec 
= cosec 
The range of principal value of cosec–1 is 
–{0} and
cosec 
= –√2
Therefore, the principal value of cosec–1(–√2) is 
.
