$W$ and $X$ are random variables and have the same probability space. If $E(WX)$ is zero then how can I prove that $\operatorname{cov} (W,X)$ is zero?

I know that $\operatorname{cov} (W,X) = E(WX)-E(w)E(X)$ but how we can decide what $E(W)$ and $E(X)$ are? We do not know that they are dependent or independent.