Sum of Reciprocals of Powers as Euler Product/Corollary 2

Corollary to Sum of Reciprocals of Powers as Euler Product
Let $\zeta$ be the Riemann zeta function.

Let $s \in \C$ be a complex number with real part $\sigma > 1$.

Then:
 * $\ds \prod_{\text {$p$ prime} } \paren {\frac {1 + p^{-s} } {1 - p^{-s} } } = \dfrac {\paren {\map \zeta s}^2} {\map \zeta {2 s} }$

where the infinite product runs over the prime numbers.