The simplified form of tan⁻¹((√(1+x²) − 1) / x) for x ≠ 0 is:

The simplified form of tan⁻¹((√(1+x²) − 1) / x) for x ≠ 0 is:

• A. tan⁻¹(x)
• B. ½ tan⁻¹(x)
• C. 2 tan⁻¹(x)
• D. cot⁻¹(x)

Answer: B) ½ tan⁻¹(x)

Explanation: Put x = tan θ. The expression becomes (sec θ − 1) / tan θ = (1 − cos θ) / sin θ = 2 sin²(θ/2) / (2 sin(θ/2) cos(θ/2)) = tan(θ/2). So, ½ θ = ½ tan⁻¹(x).