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If A + B + C = 180 deg, then the value of (sin2A + sin2B + sin2C)/(sinA + sinB + sinC) is:

1. 8*sin(A/2)*sin(B/2)*sin(C/2)
2. 4*cos(A/2)*cos(B/2)*cos(C/2)
3. 8*cos(A/2)*cos(B/2)*cos(C/2)
4. 4*sin(A/2)*sin(B/2)*sin(C/2)

Correct answer: 8*sin(A/2)*sin(B/2)*sin(C/2)

Solution

Using the two standard triangle identities for the numerator and denominator, the ratio simplifies to 8*sin(A/2)*sin(B/2)*sin(C/2).

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