Question 3
Find all functions $f:\mathbb R\to\mathbb R$ such that
(i) $f(2u)=f(u+v)f(v-u)+f(u-v)f(-u-v)$ for all $u,v\in\mathbb R$, and
(ii) $f(u)\ge0$ for all $u\in\mathbb R$.
(i) $f(2u)=f(u+v)f(v-u)+f(u-v)f(-u-v)$ for all $u,v\in\mathbb R$, and
(ii) $f(u)\ge0$ for all $u\in\mathbb R$.