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 2sin
= θ
We know sin
∴ 2sin
= 2
⇒ 2sin
= √2
∴ The question becomes sec–1(√2)
Now,
Let sec–1(√2) = y
⇒ sec y = √2
⇒ sec
= √2
The range of principal value of sec–1is [0, π ]–{
}
And sec
= √2
∴ The principal value of sec–1(2sin
) is 
.
