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If A + B + C = 180 deg, prove the relation sin²(A) + sin²(B) - sin²(C) = 2 sin(A) sin(B) cos(C). Which statement is correct?

1. The identity holds for every triangle (A+B+C = 180 deg).
2. The identity is false.
3. It holds only for a right-angled triangle.
4. It holds only for an equilateral triangle.

Correct answer: The identity holds for every triangle (A+B+C = 180 deg).

Solution

Converting squares to double angles and using A+B = 180-C reduces the left side to 2 sinA sinB cosC.

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