IMO 1985 LL VIE96

Determine all functions f : R oR satisfying the following two

IMO 1985 LL VIE96

Origin: VIE

Problem

Determine all functions f : R \toR satisfying the following two conditions: (a) f(x + y) + f(x −y) = 2f(x)f(y) for all x, y \inR, (b) limx\to\inftyf(x) = 0.