alleryMaximum value of sin(2 arctan(x)) over real x:
A2
B0
C1 (achieved at x = 1, gives sin 2θ = 1 with θ = π/4)
D-1
Answer & Solution
Correct answer: C. 1 (achieved at x = 1, gives sin 2θ = 1 with θ = π/4)
sin(2 arctan(x)) = 2x/(1+x²).
**Derivative:** (2(1+x²) - 2x(2x))/(1+x²)² = (2 - 2x²)/(1+x²)².
Critical at x = ±1. At x = 1: value = 2/2 = 1. Maximum = 1.
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