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Functional relation

Source: Finnish Mathematics Competition 2002, Final Round, Problem 1

November 14, 2011
functiontrigonometryalgebra unsolvedalgebra

Problem Statement

A function ff satisfies f(cos⁡x)=cos⁡(17x)f(\cos x) = \cos (17x) for every real xx. Show that f(sin⁡x)=sin⁡(17x)f(\sin x) =\sin (17x) for every x∈R.x \in \mathbb{R}.
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