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(sin x) = f(cos x) polynomial

Source: Indian Postal Coaching 2009 set 4 p3

May 26, 2020
polynomialtrigonometryalgebra

Problem Statement

Find all real polynomial functions f:R→Rf : R \to R such that f(sin⁡x)=f(cos⁡x)f(\sin x) = f(\cos x).
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