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If A, B, and C are the three angles of a triangle, what is the value of sin²A + sin²B + sin²C − 2 cosA cosB cosC?

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

Using A+B+C=pi, sin^2A+sin^2B+sin^2C = 2 + 2cosA cosB cosC, so sin^2A+sin^2B+sin^2C - 2cosA cosB cosC = 2.

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