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Simplify: arcsin(sin(x)) for x ∈ [π/2, π]:
A-x
Bπ - x (since sin(π-x) = sin x and π - x ∈ [0, π/2])
Cx
Dπ + x
Answer & Solution
Correct answer: B. π - x (since sin(π-x) = sin x and π - x ∈ [0, π/2])
For x ∈ [π/2, π]: sin x = sin(π - x), and π - x ∈ [0, π/2] which IS in arcsin's principal range. So arcsin(sin x) = π - x.
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