How can we pray if there are things in prayer we do not believe?
Many people treat prayer like a treatise, picking through the book for doctrinal points. While we should not assert things we do not believe, prayer is not philosophy. Prayer is poetry. The sound of the words, the rhythm and cadence, are integral to prayer. "Sometimes too hot the eye of heaven shines" is not the same as "Some days are sweltering." The 'content' is loosely the same, but one is poetry.
When we say "This is the Torah God gave to Moses" as we hold the Torah aloft in the Sabbath service, we can recite that declaration even if we have doubts that the Torah is the literal, verbatim word of God. The declaration is deeper than the definition. It is a current carried from the past into the future. "Beauty is truth and truth beauty -- that is all ye know on earth and all ye need to know" famously declared Keats. Clearly not if you have to balance a checkbook. But we do not read poetry for information and we do not pray from the newspaper.
Over the years a prayerbook or hymnal becomes a vessel into which the aspirations and sometimes frustrations of the ages have been poured. They are the resource. Prayer connects us to one another, in shared longing for our own lives and for the world. Singing together changes the spiritual atmosphere. When one of us is sad, or broken, or cannot sing, the voice of another will lift him up and help soothe his spirit. It little matters if the words on the page would find their way into a list of approved beliefs.
We pray to heal our hearts and stir our souls. Check your caveats at the door. In here, we reach toward God.