My question is, in Ramadhaan, are we supposed to pray Taraaweeh and Tahajjud both? Or praying Taraaweeh suffices for Tahajjud?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

It is not an obligation on a Muslim neither to perform Taraaweeh prayers nor Tahajjud [performing night prayers after having slept] prayers. Both types of prayers are desirable and not obligatory. So, whoever performs Taraaweeh prayers, it is good for him, and whoever performs Tahajjud prayers, it is good for him; but if a person performs both prayers, then that is even better. Please refer to Fataawa 83343, 90601 and 83333 on the difference between Taraaweeh and Tahajjud prayers.

Allaah Knows best.