IMO 1978 LL GDR29

Origin: GDR

Problem

(Variant of GDR 4) Given a nonconstant function f : R+ \toR such that f(xy) = f(x)f(y) for any x, y > 0, find functions c, s : R+ \toR that satisfy c(x/y) = c(x)c(y)−s(x)s(y) for all x, y > 0 and c(x)+s(x) = f(x) for all x > 0.