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2 arcsin(x) for |x| ≤ 1/√2 equals:
Aarcsin(2x²)
BBoth B and C
Carcsin(2x sqrt(1-x²)) (double-angle formula)
Darccos(1-2x²)
Answer & Solution
Correct answer: B. Both B and C
sin(2 arcsin x) = 2 sin θ cos θ = 2x sqrt(1-x²). Also cos(2θ) = 1 - 2 sin²θ = 1 - 2x². So 2 arcsin(x) = arcsin(2x sqrt(1-x²)) = arccos(1-2x²) — both valid representations within domain.
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