This is the Famous ‘Jaya mantra”. Hanuman announces his presence in Ashokvan to get the attention of Ravana.
The authority with which he announces himself is indeed contagious. Seemingly he achieves success by announcing himself as the servant of Rama . He lets go a roar ” Victory to Rama”. That roar itself disheartens the enemies!
The mystique of these slokas is that it is sung in First person. Hanuman says it in First person. “Dasoham Kausalendrasya…. When we recite we are automatically reciting in first person !! . I suppose that sentence making ourselves a Rama Bhaktas and hailing the victory of Rama provides a contagious self belief leading to victory.
We might as well recite loudly with vigour.
The energy it gives is worth its purpose.
Ramayana Jaya Mantram in Hindi:
जयत्यतिबलो रामो लक्ष्मणश्च महाबलः |
राजा जयति सुग्रीवो राघवेणाभिपालितः ॥
दासोहं कोसलेन्द्रस्य रामस्याक्लिष्टकर्मणः |
हनुमान् शत्रुसैन्यानां निहन्ता मारुतात्मजः ॥
न रावण सहस्रं मे युद्धे प्रतिबलं भवेत् |
शिलाभिस्तु प्रहरतः पादपैश्च सहस्रशः ॥
अर्धयित्वा पुरीं लङ्कामभिवाद्य च मैथिलीं |
समृद्धार्धो गमिष्यामि मिषतां सर्वरक्षसाम् ॥