Brother following hadiths may help u to understand about Taraweeh and Tahajjud during the month of Ramadhan
Bukhari: Volume 3, Book 32, Number 230:
Narrated Abu Salama bin 'Abdur Rahman:
that he asked 'Aisha "
How was the prayer of Allah's Apostle in Ramadan?" She replied, "He did not pray more than eleven Rakat in
Ramadan or in any other month. He used to pray four Rakat ---- let alone their beauty and length----and then he would pray four ----let alone their beauty and length ----and then he would pray three Rakat (Witr)." She added, "I asked, 'O Allah's Apostle! Do you sleep before praying the Witr?' He replied, 'O 'Aisha! My eyes sleep but my heart does not sleep."
Muslim: Book 4, Number 1607:
Abu Salama b. Abd al-Rahman asked 'A'isha about the (night)
prayer of the Messenger of Allah (may peace be upon him) during the month of Ramadan. She said: The Messenger of Allah (may peace be upon him) did not observe
either in Ramadan or in other months more than eleven rak'ahs (of the night prayer). He (in the first instance) observed four rak'ahs. Ask not about their excellence and their length (i.e. these were matchless in perfection and length). He again observed four rak'ahs, and ask not about their excellence and their length. He would then observe three rak'ahs (of the Witr prayer). 'A'isha again said: I said: Messenger of Allah, do you sleep before observing the Witr prayer? He said: O 'A'isha, my eyes sleep but my heart does not sleep.

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