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:
We can write,
tan
= tan (2π – 
)
tan(2π – θ )
= tan(–θ)
= –tanθ
∴ tan
becomes –tan
–tan
= –
⇒ 2tan
= –
∴ The question converts to cosec–1(–
)
Let cosec–1
= y
⇒ cosec y = 
= cosec
The range of principal value of cosec–1 is 
–{0}
and cosec
Therefore, the principal value of cosec–1
is 
.
