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Very beautiful functional equation involving trigonometry

Source: Moldova TST for IMO 2020

March 7, 2020
algebrafunctional equationfunctiontrigonometry

Problem Statement

Find all functions f:[−1,1]→R,f:[-1,1] \rightarrow \mathbb{R}, which satisfy f(sin⁡x)+f(cos⁡x)=2020f(\sin{x})+f(\cos{x})=2020 for any real number x.x.
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