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trigonometric equation in two variables

Source: Romanian TST 1978, Day 3, P4

September 30, 2018
trigonometrytrigonometric equationequationsalgebra

Problem Statement

Solve the equation sin⁡xsin⁡2x⋯sin⁡nx+cos⁡xcos⁡2x⋯cos⁡nx=1, \sin x\sin 2x\cdots\sin nx+\cos x\cos 2x\cdots\cos nx =1, for n∈N n\in\mathbb{N} and x∈R. x\in\mathbb{R} .
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