Let $\pi:X\rightarrow Y$ be a double cover of complex varieties and take $L$ holomorphic line bundle on $Y$.

I read that there are the isomorphisms

1) $H^p(X,\mathcal{O}_X)\simeq H^p(Y,\pi_*\mathcal{O}_X)$

2) $H^p(Y,\mathcal{O}_Y\oplus L)\simeq H^p(Y,\mathcal{O}_Y)\oplus H^p(Y,L)$

How can i prove them?