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Simplest form of tan⁻¹[(√(1 + x²) - 1)/x], x ≠ 0, is
A2 tan⁻¹x
Btan⁻¹(2x)
Ctan⁻¹x
D(1/2) tan⁻¹x
Answer & Solution
Correct answer: D. (1/2) tan⁻¹x
With x = tan θ, the ratio becomes (sec θ - 1)/tan θ = tan(θ/2), so the result is θ/2 = (1/2) tan⁻¹x.
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