It is mentioned in hadith that the holy Prophet Muhammad (صلى الله عليه وسلم) did not offer more than eight rakah in Ramadan and other days. If this eight rakah is taken as tarawih then what about the tahajjud salah of the holy Prophet Muhammad (صلى الله عليه وسلم)? Also tarawih is not offered in days other than Ramadan. Tahajjud salah may be offered after tarawih. If you want to know more details then study the book “Rakaat-e-Tarawih” by Muhaddith-e-Kabir Hadhrat Maulana Habibur Rahman Azami (رحمة الله).
Allah knows Best!
Darul Uloom Deoband