如图,四棱柱$ABCD-A_1{B}_1{C}_1{D}_1$的所有棱长都相等,$AC\cap BD=O,A_1{C}_1\cap B_1{D}_1=O_1$,四边形$AC{C}_1{A}_1$和四边形$BD{D}_1{B}_1$为矩形.
(1)证明:$O_{1}O\perp$平面;$ABCD$

(2)若$\angle CBA=60°$,求二面角$C_1-O{B}_1-D$的余弦值.