Again, not sure what belief we are discussing. The first part of the Hail Mary is scriptural; the second part is a prayer of intercession. There is nothing dogmatic about the rosary. Although there is commentary that it was given to St. Dominic, there is information floating about that the Dominicans don’t hold that. The better information seems to be that long prior to St. Dominic, laity, who were uneducated, started saying 150 Our Fathers as a mimic if you will to what the monks said - the 150 Psalms. It eventually morphed into 5 Our Fathers and 50 Hail Marys.
By belief if you mean the efficacy of the rosary, all prayers are efficacious. Certainly, if one looks at the Old Testament and observes the power and place of the queen mother to the king (often referred to as “the power behind the throne”), then one sees the importance and place which Mary has in relation to Jesus.
The rosary, like any other prayer, should be used with the understanding that we petition, God decides. Honoring Mary honors her Son.
Hope that answers your question.