Aditya Hridaya Stotra Five

त्रिराचम्य शुचिर्भूत्वा धनुरादाय वीर्यवान् ।।29।।
रावणंप्रेक्ष्य हृष्टात्मा युद्धाय समुपागमत् ।
सर्वयत्नेन महता वधे तस्य धृतो‌ऽभवत् ।।30।।

परम हर्षित और शुद्धचित्त होकर उन्होंने भगवान सूर्य की ओर देखते हुए तीन बार आदित्य ह्रदय स्तोत्र का तीन बार जप किया।
तत्पश्चात राम जी ने धनुष उठाकर युद्ध के लिए आये हुए रावण को देखा और उत्साह से भरकर सभी यत्नो से रावण के निश्चय किया।।

Aadityam Prekssya Japtvaa Tu Param Harssam-Avaaptavaan |
Trir-Aacamya Shucir-Bhuutvaa Dhanur-Aadaaya Viiryavaan ||29||
Meaning:
29.1: (Salutations to the Sun God) (Then) looking at the Sun God and reciting (this stotra), (Sri Rama) became very Happy,
29.2: Sipping Water three times and becoming purified, (Sri Rama) the valiant one, took up his Bow,Raavannam Prekssya Hrsstta-[A]atmaa Yuddhaaya Sam-Upaagamat |
Sarva-Yatnena Mahataa Vadhe Tasya Dhrto-[A]bhavat ||30||

Meaning:
30.1: (Salutations to the Sun God) (Now) The Glad-Souled (Rama) seeing Ravana approaching to wage a war, …
30.2: … collected all his Efforts and Aspirations to slay that Mighty (demon).

अथ रविरवदन्-निरीक्ष्य रामं मुदितमनाः परमं प्रहृष्यमाणः ।
निशिचरपति सङ्क्षयं विदित्वा सुरगण मध्यगतो वचस्त्वरेति।।३१।।

तब देवताओं के मध्य में खड़े हुए सूर्य देव ने प्रसन्न होकर श्री राम की ओर देखकर निशाचराज ( राक्षस के राजा ) के विनाश का समय निकट जानकर प्रसन्नता पूर्वक कहा “अब जल्दी करो”।।

Atha Ravir-Avadan-Niriikssya Raamam Mudita-Manaah Paramam Prahrssyamaannah |
Nishi-Cara-Pati-Samkssayam Viditvaa Sura-Ganna-Madhyagato Vacas-Tvare[a-I]ti ||31||

Meaning:
31.1: (Salutations to the Sun God) Then, the Sun-God (Ravi) said, looking at Rama with delighted mind and great pleasure, …
32.1: … and knowing that the time of the final destruction of the king of the Night-Movers (i.e. demons) have arrived; (The Sun-God) said amidst the group of gods: “Make Haste” (O Rama, and save the World).

।। इत्यार्षे श्रीमद्रामायणे वाल्मिकीये आदिकाव्ये युद्दकाण्डे पञ्चाधिक शततम सर्गः।।

Rama killed Ravana with a Brahmastra, the mantra was created by Lord Brahma himself later this mantra was given to Sage Agastya to be given to Lord Rama during Ramayana period. Sage Agastya himself gives the mantra to Lord Rama during exile, to help win the battle, Rama fixed that excellent arrow on the bow, and Rama reciting the key mantras invoked the Brahmastra.

As narrated in the Valmiki Ramayana Yuddha Kanda Sarga 108:
ValmikiRamayan Yuddha Sarga108