Valmiki Ramayana Ayodhya Kanda Sarga 52 Shloka 62
Original Shlokaपरितुष्टा हि सा देवी वनवासं गते मयि। राजानं नातिशङ्केत 'मिथ्यावादी'ति धार्मिकम्।।2.52.62।।
1 source checked for this shloka
मयि when I, वनवासम् dwell in the forest, गते having gone, सा देवी that queen, परितुष्टा completely satisfied, धार्मिकम् righteous, राजानम् about king Dasaratha, 'मिथ्यावादी'ति claimed to be a liar, नातिशङ्केत not have any doubt.
If queen Kaikeyi is fully satisfied that I have gone to dwell in the forest, she will no longer have any doubt and will believe that righteous king Dasaratha is not a liar.