Firstly: 

The following reports have been narrated concerning the adhkaar to be recited when bowing: 

1 – Saying “Subhaana Rabbiy al-‘Azeem (Glory be to my Lord Most Great)”, because of the report narrated by Muslim (772) from Hudhayfah (may Allaah be pleased with him) who said:

I prayed with the Prophet (peace and blessings of Allaah be upon him) one night… then he bowed and he started saying: “Subhaana Rabbiy al-‘Azeem (Glory be to my Lord Most Great).” 

2 – Saying “Subhaana Rabbiy al-‘Azeem wa bi hamdihi (Glory and praise be to my Lord Most Great)”, because of the report narrated by Abu Dawood from ‘Uqbah ibn ‘Aamir (may Allaah be pleased with him) who said:

When the Messenger of Allaah (peace and blessings of Allaah be upon him) bowed, he would say: “Subhaana Rabbiy al-‘Azeem wa bi hamdihi (Glory and praise be to my Lord Most Great)” three times, and when he prostrated he would say: “Subhaana Rabbiy al-A’laa wa bi hamdihi (Glory and praise be to my Lord Most High)” three times.

Classed as saheeh by al-Albaani in Sifat al-Salaah, p. 133. 

3 – Saying “Subbooh Quddoos Rabb ul-Malaa’ikah wa’l-Rooh (Glorified, Holy, Lord of the Angels and of the Rooh)” because of the report narrated by Muslim (487) from ‘Aa’ishah (may Allaah be pleased with her), according to which the Messenger of Allaah (peace and blessings of Allaah be upon him) used to say when bowing and prostrating: “Subbooh Quddoos Rabb ul-Malaa’ikah wa’l-Rooh (Glorified, Holy, Lord of the Angels and of the Rooh)”. 

4 – Saying: “Subhaanaka Allaahumma Rabbana wa bihamdika, Allaahumma ighfir li (Glory and praise be to You, O Allaah our Lord; O Allaah, forgive me)” because of the report narrated by al-Bukhaari (794) and Muslim (484) from ‘Aa’ishah (may Allaah be pleased with her) who said:

The Prophet (peace and blessings of Allaah be upon him) used to say when bowing and prostrating: “Subhaanaka Allaahumma Rabbana wa bihamdika, Allaahumma ighfir li (Glory and praise be to You, O Allaah our Lord; O Allaah, forgive me)”. 

5 – Saying, “Allaahumma laka raka’tu wa bika aamantu … (O Allaah, to You have I bowed and in You have I believed…)” because of the report narrated by Muslim (771) from ‘Ali ibn Abi Taalib (may Allaah be pleased with him) , according to which when the Messenger of Allaah (peace and blessings of Allaah be upon him) bowed, he would say: “Allaahumma laka raka’tu wa bika aamantu wa laka aslamtu, khasha’a laka sam’i wa basari wa mukhkhi wa ‘azmi wa ‘asabi (O Allaah, to You have I bowed and in You have I believed and to You have I submitted; my hearing, my sight, my brain, my bones and my sinews submit to You).” 

Secondly: 

The Muslim should preserve these Sunnahs that have been narrated from the Messenger (peace and blessings of Allaah be upon him), so he should say one of them sometimes and another of them sometimes. And he may combine all these adhkaar in one bowing. 

Al-Nawawi (may Allaah have mercy on him) said in al-Adhkaar (p. 86): But it is better to combine all of these adhkaar if that is possible without causing hardship to anyone else, and he should recite the tasbeehs first (those that start with the words Subhaan Allaah). If he wants to keep it short then it is mustahabb to say tasbeeh, and the minimum required is to say tasbeeh three times, but if he says it only once he will have done what is basically required for tasbeeh. If he wants to limit it to only some of the adhkaar, it is mustahabb to say some of them sometimes and others at other times and so on, so that he will have done all of them. End quote. 

It says in al-Iqnaa’, which is a Hanbali book (1/119): It is not makrooh to add something to the phrases “Rabb ighfir li (Lord forgive me) or to say more than “Subhaana Rabbiy al-‘Azeem (Glory be to my Lord Most Great)” and “Subhaana Rabbiy al-‘Ala (Glory be to my Lord Most High)” when bowing and prostrating. End quote 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said in al-Sharh al-Mumti’ (3/77), after mentioning a number of adhkaar to be said when bowing and raising the question as to whether these adhkaar may be combined or one should recite only one of them: 

This is possible. We have stated above that not all of the opening du’aa’s that have been narrated should be said at once, rather we should say one of them sometimes and another at other times, and we have quoted the evidence for that. But with regard to the adhkaar for bowing which are known to most of the scholars, they may all be recited together. End quote.

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