Find all functions such that $$\forall x,y \in \mathbb{R} \quad f(x+y)+f(x-y)=2f(x)\cos y$$
I got this question from a book. I tried substituting and assuming different values of $x$ and $y$ but ended getting nothing powerful enough to solve it. On taking $y=90^\circ$ I got a function in $x$ following periodicity of a trigonometric function. But it will be valid iff $y$ is $90^\circ$. I'm stuck. Any help would be appreciated. Thanks in advance.
