"Arcanam means worshiping Lord Visnu as one does in the temple, and vandanam means offering respectful obeisances. Man-mana bhava mad-bhakto mad-yaji mam namaskuru. Vandanam means namaskuru--offering obeisances or offering prayers."
"Vandanam. Although prayers are a part of Deity worship, they may be considered separately like the other items, such as hearing and chanting, and therefore separate statements are given herewith. The Lord has unlimited transcendental qualities and opulences, and one who feels influenced by the Lord's qualities in various activities offers prayers to the Lord. In this way he becomes successful. In this connection, the following are some of the offenses to be avoided: (a) to offer obeisances on one hand, (b) to offer obeisances with one's body covered, (c) to show one's back to the Deity, (d) to offer obeisances on the left side of the Deity, (e) to offer obeisances very near the Deity."
"Prayer means vandanam. So this is also service. Either you take all the nine different items, or you take some of them, or at least one of them, then you will make progress in spiritual life. So some of them offer prayers, just like Christians, Muhammadans, they offer prayer. So it is as good as the Hindus give service in the temple, decorates the Deity, cleanses the temple and offers food. In this way they are engaged. This is called arcanam. Arcanam is also devotional service as well as offering prayer. So by this devotional service one makes progress in spiritual life, and when he is sincere in his service, then God is within him, He takes charge of him and gives him instruction how quickly and swiftly he can approach God. So this is fact. Our... He is not hankering after our service. He is complete in Himself. He doesn't require anyone's service. But if we offer service to Him, then we become purified, and... (break) ...complete purification. We can talk with God, we can see God, we can take His instruction, as Arjuna is talking with God, personally taking His instruction and acting according to His instruction."
Philosophy Discussions, Kierkegaard
"We should always speak of Krsna in a pleasing way; then we will be benefited. Another name for Krsna is Uttamasloka, which indicates that He is worshiped by the best selected words. It is not that we should use any words we choose. There are many prayers in the Vedic scriptures and also in the Bible and Koran. Although the Christians and Muhammadans do not worship the Deity, they offer prayers to the Lord, and that is also bhakti. Arcanam vandanam."
Teachings of Lord Kapila, Verse 35
"According to great learned scholars, the whole Bhagavad-gita contains many authorized prayers, especially in the Eleventh Chapter, where Arjuna prays to the universal form of the Lord. Similarly, in the Gautamiya-tantra all the verses are called prayers. Again, in Srimad-Bhagavatam there are hundreds of prayers to the Lord. So a devotee should select some of these prayers for his recitation. In Skanda Purana the glories of these prayers are stated as follows: "Devotees whose tongues are decorated always with prayers to Lord Krsna are always given respect even by the great saintly persons and sages, and such devotees are actually worshipable by the demigods."
Those who are less intelligent want to worship different demigods for some material gain rather than worship Krsna. But here it is stated that a devotee who is always engaged in offering prayers to the Lord is worshipable even by the demigods themselves. The pure devotees have nothing to ask from any demigod; rather, the demigods are anxious to offer prayers to the pure devotees.
In the Nrsimha Purana it is stated, "Any person who comes before the Deity of Lord Krsna and begins to chant different prayers is immediately relieved from all the reactions of sinful activities and becomes eligible, without any doubt, to enter into the Vaikunthaloka."
Nectar of Devotion, Chapter 9
Bhaktivedanta Book Trust. HDG A.C. Bhaktivedanta Swami Srila Prabhupada.