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Question
Find the principal value of the following: `sin^-1 (1/2)`
Solution
The principal value branch of `sin^-1 x "is" [- pi/2, pi/2]`.
Let `sin^-1 (1/2) = α, "where" (-pi)/(2) ≤ α ≤ pi/(2)`
∴ `sin α = 1/2 = sin pi/(6)`
∴ α = `pi/(6) ...[ ∵ - pi/2 ≤ pi/6 ≤ pi/2 ]`
∴ the principal value of `sin^-1 (1/2) "is" pi/(6)`.
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