Rabbi Miller writes about the connection between bitachon and prayer in Sing, You Righteous (#499): We must exert ourselves on behalf of our health and our livelihood, else we would be guilty of neglecting the welfare of a fellow-Israelite. This guilt would not be mitigated by the fact that the Israelite is ourself; on the contrary, the closer relationship imposes greater obligation to guard his health and to provide his needs. But if we strive to do this by our own efforts, how are we able to continue to feel that G-d does everything, and that He alone protects us and gives us our needs? Our deeds constantly contradict bitachon.The answer is: by means of tefillah. If one persists in requesting beforehand that G-d help him in his efforts, and he persists also in thanking G-d afterward, then he thereby is able to gain the awareness of the Creator’s control over everything. Before any act on behalf of our health or sustenance, we first seek G-d’s aid to prosper our deeds; and after we perform any act for ourselves, or after we see that we are well and are supplied with our necessities, we express our gratitude to Him. By bakashah (request) and by hodaah (thanks) we constantly demonstrate the principle of His kingship over everything, and we gradually gain in awareness of the Presence of the Creator. Prayer is the way we address the constant tension between hishtadlus and bitachon. By praying for our needs beforehand we demonstrate our awareness that our destiny is in G-d’s hands, and by thanking Him after our request is fulfilled we further demonstrate that same awareness. The more we pray to Him and thank Him with proper intent, the more we deepen our awareness that He is in control of our future and present just as He has been over our past, and the more we deepen our bitachon.

Miller, Rabbi Avigdor. Rav Avigdor Miller on Emunah and Bitachon . The Judaica Press, Inc.. Kindle Edition.