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Bosnia and Herzegovina TST 1996 Day 2 Problem 1

Source: Bosnia and Herzegovina Team Selection Test 1996

September 20, 2018

algebrafunctional equation

Problem Statement

Solve the functional equation

f(x+y)+f(x-y)=2f(x)\cos{y}

where

x,y \in \mathbb{R}

and

f : \mathbb{R} \rightarrow \mathbb{R}