My question is similar to this, but not identical. I believe the following to be true, but I'd like a reference.
Given (quasicoherent?) sheaves of $\mathcal O_X$ modules $E$ and $F$ on a projective variety $X$, $$ H^n(X, E\otimes F) \cong \bigoplus_{p+q=n} H^p(X, E) \otimes H^q(X, F). $$
Is this true, and what is a good reference or counterexample? If true, is quasicoherent necessary?