Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 3 of Exercise 4.5
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3
For the principal values, evaluate the following:
Let,
Sin–1
= y
⇒ sin y = 
⇒ –sin y = 
⇒ –sin 
As we know sin(–θ) = –sinθ
∴ –sin 
= sin 
The range of principal value of sin–1 is 
and sin 
Therefore, the principal value of Sin–1
is 
….(1)
Let,
cosec–1
= z
⇒ cosec z = 
⇒ –cosec z = 
⇒ –cosec 
As we know cosec(–θ) = –cosecθ
∴ –cosec 
= cosec 
The range of principal value of cosec–1 is is 
–{0} and
cosec 
Therefore, the principal value of cosec–1
is 
….(2)
From (1) and (2) we get
⇒ 
= 
