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y(x)=cos (cos x)+ a sin (sin x) is periodic (VII Soros Olympiad 2000-01 R1 11.1)

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July 29, 2021
functionperiodic functionPeriodicity

Problem Statement

Prove that for any aa the function y(x)=cos⁡(cos⁡x)+a⋅sin⁡(sin⁡x)y (x) = \cos (\cos x) + a \cdot \sin (\sin x) is periodic. Find its smallest period in terms of aa.
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