Question 36
Find all functions $f: \mathbb{R} \to \mathbb{R}$, such that:
1) For all real $x, y$ the following equality holds
$$
f(2x) = f(x+y)f(y-x) + f(x-y)f(-x-y).
$$
2) $f(x) \ge 0$ for all $x$.
1) For all real $x, y$ the following equality holds
$$
f(2x) = f(x+y)f(y-x) + f(x-y)f(-x-y).
$$
2) $f(x) \ge 0$ for all $x$.