1972 IMO Problems/Problem 5
Let f and g be real-valued functions defined for all real values of x and y; and satisfying the equation
f(x+y)+f(x-y)=2f(x)g(y)
for all x, y. Prove that if f(x) is not identically zero, and if |f(x)| < or = 1 for all x; then |g(y)| < or = 1 for all y:
