Home Competitions ILL 1976 Problem 49
Determine whether there exist 1976 1976 1976 α , β , γ , \alpha, \beta, \gamma, α , β , γ , sin α + sin β + sin γ cos α + cos β + cos γ = 12 7 and sin α sin β sin γ = 12 25 \frac{\sin \alpha + \sin\beta + \sin\gamma}{\cos \alpha + \cos \beta + \cos \gamma}=\frac{12}{7}\text{ and }\sin \alpha \sin \beta \sin \gamma =\frac{12}{25} cos α + cos β + cos γ sin α + sin β + sin γ = 7 12 and sin α sin β sin γ = 25 12
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