If $\mathrm{f}(\mathrm{x})$ satisfies the functional equation $f(x+y)+f(x-y)=2 f(x) f(y) \forall x,

Question

If $\mathrm{f}(\mathrm{x})$ satisfies the functional equation $f(x+y)+f(x-y)=2 f(x) f(y) \forall x, x$ then $\mathrm{f}(\mathrm{x})$ is

Professor PC Thomas Classes · Answer

$ \begin{aligned} & \mathrm{f}(\mathrm{y}+\mathrm{x})+\mathrm{f}(\mathrm{y}-1)=\alpha \mathrm{f}(\mathrm{y}) \mathrm{f}(\mathrm{x}) \ & \Rightarrow \mathrm{f}(\mathrm{x}-\mathrm{y})=\mathrm{f}(\mathrm{y}-\mathrm{x}) \end{aligned} $