allerySimplify arctan(sin x / (1+cos x)) for x ∈ (-π, π):
Ax²
Bx/2 (use half-angle: sin x/(1+cos x) = tan(x/2))
Cx
Darctan(x)
Answer & Solution
Correct answer: B. x/2 (use half-angle: sin x/(1+cos x) = tan(x/2))
**Half-angle:** sin x = 2 sin(x/2) cos(x/2), 1 + cos x = 2 cos²(x/2).
Ratio = sin(x/2)/cos(x/2) = tan(x/2).
For x/2 ∈ (-π/2, π/2), arctan(tan(x/2)) = x/2.
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