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If A + B + C = 180 deg, then the value of sin(B + 2C) + sin(C + 2A) + sin(A + 2B) equals:

1. 4*sin((B - C)/2)*sin((C - A)/2)*sin((A - B)/2)
2. 4*cos((B - C)/2)*cos((C - A)/2)*cos((A - B)/2)
3. -4*sin((B - C)/2)*sin((C - A)/2)*sin((A - B)/2)
4. sin A + sin B + sin C

Correct answer: 4*sin((B - C)/2)*sin((C - A)/2)*sin((A - B)/2)

Solution

Each term reduces to a negative sine of an angle difference, and combining them with sum-to-product yields the symmetric product form.

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