prove that the space $C^{\infty}(R_{+}^n)\cap W^{1,2}(R_{+}^n)$ is dense in $W^{1,2}(R_{+}^n)$

Question

I already know that as $C^{\infty}_c(R^n)$ is dense in $W^{1,2}(R^n)$, but I don't know why the space $C^{\infty}(R_{+}^n)\cap W^{1,2}(R_{+}^n)$ is dense in $W^{1,2}(R_{+}^n)$

Is the statement true and why?

Thank you!