Did David believe in one God?...or a triune God?

Question: Did David believe in one God?...or a triune God?

Answer:

Triune God? No

There is not a single text in the entire Bible that supports the idea that David believed in a triune God.

One God? Yes

David, the king of Israel, believed in only one true God, Yahuwah Elohim. And not only David, but all of Israel, too.

Then said David to the Philistine, Thou comest to me with a sword, and with a spear, and with a shield: but I come to thee in the name of the LORD [Yahuwah] of hosts, the God of the armies of Israel, whom thou hast defied. (1 Samuel 17:45)
And Jonathan said unto David, O LORD God [Yahuwah Elohim] of Israel, when I have sounded my father about to morrow any time, or the third day, and, behold, if there be good toward David, and I then send not unto thee, and shew it thee; (1 Samuel 20:12)

Yahuwah was the God of Israel:

The LORD [Yahuwah] do so and much more to Jonathan: but if it please my father to do thee evil, then I will shew it thee, and send thee away, that thou mayest go in peace: and the LORD [Yahuwah] be with thee, as he hath been with my father. (1 Samuel 20:13)
Then said David, O LORD God [Yahuwah Elohim] of Israel, thy servant hath certainly heard that Saul seeketh to come to Keilah, to destroy the city for my sake. (1 Samuel 23:10)
And David said to Abigail, Blessed be the LORD God [Yahuwah Elohim] of Israel, which sent thee this day to meet me: (1 Samuel 25:32)
And David was greatly distressed; for the people spake of stoning him, because the soul of all the people was grieved, every man for his sons and for his daughters: but David encouraged himself in the LORD [Yahuwah] his God.
So do God to Abner, and more also, except, as the LORD [Yahuwah] hath sworn to David, even so I do to him; (2 Samuel 3:9)
And David went on, and grew great, and the LORD God [Yahuwah Elohim] of hosts was with him. (2 Samuel 5:10)

Conclusion:
King David believed in the one true God, Yahuwah Elohim of hosts.