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max of V_n = sin x_1 cos x_2 +sin x_2 cos x_3 +...+sin x_n cos x_1

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1997 p5

February 20, 2020
trigonometrymaxfunctionalgebrainequalities

Problem Statement

For a given integer n≥2n \ge 2, find the maximum possible value of Vn=sin⁡x1cos⁡x2+sin⁡x2cos⁡x3+...+sin⁡xncos⁡x1V_n = \sin x_1 \cos x_2 +\sin x_2 \cos x_3 +...+\sin x_n \cos x_1, where x1,x2,...,xnx_1,x_2,...,x_n are real numbers.
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