Correct answer: (B) They are pairwise independent.
Explanation
Integrating over any coordinate kills the sine term because its integral over a full period is zero. Every pair therefore has constant density1/(4π²), the product of two uniform marginal densities. Thus pairwise independence holds, B. The full joint sine term prevents mutual independence; Var(X₁+X₂)=2π²/3, notπ².
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