Valmiki Ramayana Sundara Kanda Sarga 56 Shloka 8
Original Shlokaएवमाश्वास्य वैदेहीं हनुमान् मारुतात्मजः। गमनाय मतिं कृत्वा वैदेहीमभ्यवादयत्।।5.56.8।।
1 source checked for this shloka
मारुतात्मजः son of the Windgod, हनुमान् Hanuman, वैदेहीम् to Vaidehi, एवम् in that way, आश्वास्य having consoled, गमनाय to depart, मतिम् his mind, कृत्वा after deciding, वैदेहीम् to Vaidehi, अभ्यवादयत् respectfully saluted.
Hanuman, son of the Windgod having consoled Vaidehi, saluted her respectfully and decided to depart.