If sin⁻¹(2a/(1+a²)) + cos⁻¹(1−b²)/(1+b²) = 2tan⁻¹x, then x equals:

If sin⁻¹(2a/(1+a²)) + cos⁻¹(1−b²)/(1+b²) = 2tan⁻¹x, then x equals:

• A. (a−b)/(1+ab)
• B. (a+b)/(1−ab)
• C. (a+b)/(1+ab)
• D. (a−b)/(1−ab)

Answer: B) (a+b)/(1−ab)

Explanation: sin⁻¹(2a/(1+a²)) = 2tan⁻¹a for |a|≤1. cos⁻¹((1−b²)/(1+b²)) = 2tan⁻¹b for b≥0. Sum = 2tan⁻¹a+2tan⁻¹b = 2tan⁻¹((a+b)/(1−ab)) = 2tan⁻¹x. So x = (a+b)/(1−ab).