The principal value of sin⁻¹\(\frac{1}{\sqrt{2}}\) is equal to which of the following?

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Question

This question was previously asked in

Bihar STET Paper I: Mathematics (Held In 2019 - Shift 1)

Answer 1

Calculations:

sin(2nπ +- π/4) = 1/√2

Hence, sin−1\(\frac{1}{√{2}}\) = sin^-1(sin(2nπ +- π/4)) = 1/√2

But the principle value of sin^-1lies from (-π π)

Hence, The Principle value of sin−1\(\frac{1}{\sqrt{2}}\) = π/4

Hence, The Correct Answer is option 1 .

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