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f(sin x )+ a f(cos x) = cos 2x

Source: 2011 Belarus TST 1.1

November 7, 2020
algebrafunctional equationtrigonometryfunctional

Problem Statement

Find all real aa such that there exists a function f:R→Rf: R \to R satisfying the equation f(sin⁡x)+af(cos⁡x)=cos⁡2xf(\sin x )+ a f(\cos x) = \cos 2x for all real xx.
I.Voronovich
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