Solve the equation $ \sin x\sin 2x\cdots\sin nx+\cos x\cos 2x\cdots\cos nx =1, $ for $ n\in\mathbb{N} $ and $ x\in\mathbb{R} . $
Problem
Source: Romanian TST 1978, Day 3, P4
Tags: trigonometry, trigonometric equation, equations, algebra
Source: Romanian TST 1978, Day 3, P4
Tags: trigonometry, trigonometric equation, equations, algebra
Solve the equation $ \sin x\sin 2x\cdots\sin nx+\cos x\cos 2x\cdots\cos nx =1, $ for $ n\in\mathbb{N} $ and $ x\in\mathbb{R} . $