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^{–1}is [0, π ]–{}

And sec = √2

∴ The principal value of sec^{–1}(2sin) is .

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