Problem #PRU-116563

Problems Algebra Trigonometry Identical transformations (trigonometry) Methods Proof by contradiction Calculus Real numbers Rational and irrational numbers

15–16 2.0

Problem

Does there exist a real number $α$ such that the number $\cos α$ is irrational, and all the numbers $\cos 2 α$ , $\cos 3 α$ , $\cos 4 α$ , $\cos 5 α$ are rational?

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