If x < 0, the value of cos⁻¹((1−x²)/(1+x²)) is equal to:

If x < 0, the value of cos⁻¹((1−x²)/(1+x²)) is equal to:

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

Answer: B) −2 tan⁻¹(x)

Explanation: For x < 0, put x = tan θ where θ is in (−π/2, 0). (1−x²)/(1+x²) = cos 2θ. cos⁻¹(cos 2θ) = −2θ since 2θ < 0 and cos⁻¹ returns a positive value. So −2θ = −2 tan⁻¹(x).