Answer:
Option A.)
The answer is 1/√3
Step-by-step explanation:
3sin⁻¹ (2x/1 + x²) - 4cos⁻¹ (1 - x²/1 + x²) + 2tan⁻¹ (2x/1 - x²) = π/3
Put x = tanθ
3sin⁻¹ (2tanθ/1 + tan2θ) - 4cos⁻¹ (1 - tan2θ/1 + tan2θ) + 2tan⁻¹ (2tanθ/1 - tan2θ) = π/3
3sin⁻¹ (sin2θ) - 4cos⁻¹ (cos2θ) + 2tan⁻¹ (tan2θ) = π/3
3.2θ - 4.2θ + 2.2θ = π/3
⇒ 2θ = π/3
⇒ θ = π/6
∴ tan-1x = π/6 ⇒ x = tan (π/6) = 1/√3
Thus, The answer is 1/√3
-TheUnknownScientist 72
