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If A + B + C = 180 deg, prove that cos²(A) + cos²(B) - cos²(C) = 1 - 2 sin(A) sin(B) cos(C). What does the left-hand side equal?

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

Correct answer: 1 - 2 sin(A) sin(B) cos(C)

Solution

Converting cos² to double angles and using A + B + C = 180 deg leads to the identity equalling 1 - 2 sin A sin B cos C.

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