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If A + B + C = 180 deg, prove that sin 2A + sin 2B - sin 2C = 4 cos A cos B sin C.

1. True (identity holds when A + B + C = 180 deg)
2. Equals 4 sin A sin B cos C
3. Equals 4 sin A sin B sin C
4. Equals zero

Correct answer: True (identity holds when A + B + C = 180 deg)

Solution

Sum-to-product gives 2 sin(A+B)cos(A-B) - sin 2C; using A+B = 180-C (so sin(A+B)=sin C) and factoring out 2 sin C leads to 4 cos A cos B sin C.

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