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Given that α, β, γ, and θ are the smallest positive angles in increasing order for which their sine values equal a positive constant k, what is the result of 4 sin(α/2) + 3 sin(β/2) + 2 sin(γ/2) + sin(θ/2)?

1. 2√(1−k)
2. 2√(1+k)
3. 2√k
4. None of the above

Correct answer: 2√(1+k)

Solution

The result of the expression 4 sin(α/2) + 3 sin(β/2) + 2 sin(γ/2) + sin(θ/2) is 2√(1+k), which can be derived by applying trigonometric identities and analyzing the relationships between the angles.

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