Can I perform my taraweeh prayer while listening to Quran on audio tape?
All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad  is His slave and Messenger.
  is His slave and Messenger.
If you mean whether listening to the Quran from a cassette can substitute reciting the Quran yourself in prayer, then this is unlawful and any prayer done in such a way is invalid.
But if you mean reciting the Quran yourself in prayer while a Quran cassette is played where you are praying, then there is no objection to that. However, it is desirable for the praying person to avoid anything that could attract his/her attention while praying.
For more benefit, please refer to Fataawa 278629, 124837, and 127409.
Allah knows best.
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