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For a triangle PQR, what is the smallest possible value of the expression cos(P + Q) + cos(Q + R) + cos(R + P) ?

1. -(3)/(2)
2. (5)/(3)
3. -(5)/(3)
4. (3)/(2)

Correct answer: -(3)/(2)

Solution

The smallest possible value of the expression cos(P + Q) + cos(Q + R) + cos(R + P) is -3/2, which can be derived by using trigonometric identities to simplify the expression into -cosR - cosP - cosQ and then applying the properties of cosine functions in a triangle.

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