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For angles α, β, γ all lying in the interval (0, π/2), the value of (sin(α+β+γ))/(sinα+sinβ+sinγ) is

1. less than 1
2. greater than 1
3. equal to 1
4. none of the above

Correct answer: less than 1

Solution

Using sin(a+b) < sin a + sin b for acute angles repeatedly, sin(a+b+g) is strictly less than sin a + sin b + sin g, so the ratio is always less than 1.

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