How to prove $\Phi_w(x)=\cos (w^T x+b)$ is outside the RKHS associated with the Gaussian kernel function$K(x,y)=\exp(-\frac{||x-y||^2}{2\sigma})$?

Question

How to prove $\Phi_w (x)=\cos (w^T x+b)$ is outside the RKHS ( Reproducing Kernel Hilbert Space) associated with the Gaussian kernel function$K(x,y)=\exp(-\frac{||x-y||^2}{2\sigma})$？