Is it prescribed for the imam to recite tasbih in the night prayer when he reads (Glorified is the name of your Lord, the Most High)?
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Question:
He says: Honorable Shaykh, may Allah grant you success, if the imam reads in the night prayer, does he read "Glorified," is it prescribed for him to recite tasbih?
Answer:
It is tasbih; reciting it is tasbih, so he does not need to recite tasbih separately. And this has not been reported either, as I mentioned to you. Yes.
He says: Honorable Shaykh, may Allah grant you success, if the imam reads in the night prayer, does he read "Glorified," is it prescribed for him to recite tasbih?
Answer:
It is tasbih; reciting it is tasbih, so he does not need to recite tasbih separately. And this has not been reported either, as I mentioned to you. Yes.
Source
قناة «العلامة الدكتور صالح الفوزان»، [3979- 4717] هل يشرع للإمام التسبيح في صلاة الليل إذا قرأ (سبح اسم ربك الأعلى)؟ - الشيخ صالح الفوزان — youtube.com
The Arabic text is a machine transcription of the audio recording.