MathDB
Sines and Cosines - [ILL 1977]

Source:

January 11, 2011
trigonometryfunctioninequalitiesinductionalgebra unsolvedalgebra

Problem Statement

Let x1,x2,…,xn (n≥1)x_1, x_2, \ldots , x_n \ (n \geq 1) be real numbers such that 0≤xj≤π, j=1,2,…,n.0 \leq x_j \leq \pi, \ j = 1, 2,\ldots, n. Prove that if ∑j=1n(cos⁡xj+1)\sum_{j=1}^n (\cos x_j +1) is an odd integer, then ∑j=1nsin⁡xj≥1.\sum_{j=1}^n \sin x_j \geq 1.
Back to ProblemsView on AoPS