Book: RD Sharma - Mathematics (Volume 1)
Chapter: 4. Inverse Trigonometric Functions
Subject: Maths - Class 12th
Q. No. 1 of Exercise 4.4
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1
Find the principal values of each of the following:
Let us assume 2tan
= θ
We know tan
= –1
∴ 2tan
= 2(–1)
⇒ 2tan
= –2
∴ The question converts to sec–1(–2)
Now,
Let sec–1(–2) = y
⇒ sec y = –2
= – sec
= 2
= sec
= sec
The range of principal value of sec–1is [0, π]–{
}
and sec
= –2
∴ The principal value of sec–1(2tan
) is 
