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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
.