If he catches up with the imam when he is bowing, what should he do?
Question

If I enter the mosque and the imam is bowing, if I bow with him will that rak’ah count for me, even though I have not recited al-Faatihah? Should I say one takbeer or two?.
Praise be to Allah.Firstly: 
If a person enters the mosque when the imam is bowing, he should bow with him, and his will have caught up with the rak’ah if he joins the imam when he is bowing, even if he did not bow fully until after the imam stands up. Imam Abu Dawood said: I heard Ahmed being asked about a man who catches up with the imam when he is bowing; he says takbeer and bows, then the imam stands up. He said: If he placed his hands firmly on his knees before the imam stood up, then he has caught up with the rak’ah.  End quote. 
See: Masaa’il al-Imaam Ahmad by Abu Dawood, p. 35; Haashiyat al-Rawd, by Ibn Qaasim, 2/275; al-Majmoo, 4/215. 
Then he should be at ease in bowing, and rise from bowing, and follow his imam. 
Shaykh Ibn Baaz said: If a person catches up with the imam when he is bowing, that rak’ah counts for him, even if he does not say the tasbeeh until after the imam has stood up. End quote. 
Majmoo’ Fataawa Ibn Baaz, 11/245-246 
Secondly: 
If he catches up with him when he is bowing, then one takbeer is sufficient, i.e., the opening takbeer counts for the takbeer of bowing too. That was narrated from Zayd ibn Thaabit, Ibn ‘Umar, Sa’eed, ‘Ata’, al-Hasan and Ibraaheem al-Nakha’i. It was also the view of the four imams (Abu Haneefah, Maalik, al-Shaafa’i and Ahmad). Abu Dawood said: I said to Ahmad: What if I catch up with the imam when he is bowing? He said: One takbeer is sufficient for you. End quote. 
Masaa’il al-Imam Ahmad, p. 35 
That is because the time for bowing is usually too short to combine two takbeers, and because it is combining two acts of worship of the same type in the same place. The intention to bow does not cancel out the intention to start praying. So the pillar or essential part, namely the opening takbeer, suffices for the obligatory duty, namely the takbeer for bowing, just as tawaaf al-ifaadah suffices for the farewell tawaaf if it is done last of all. 
See al-Mughni, 2/183; al-Qawaa’id by Ibn Rajab, number 18. 
If a person can say two takbeers, one for starting the prayer and one for bowing, that is better. Abu Dawood said: I said to Ahmad: Is saying two takbeers dearer to you? He said: If he says two takbeers there is no dispute on the matter. End quote. 
Masaa’il al-Imam Ahmad, p. 35 
Shaykh Ibn Baaz was asked: If a person joins the prayer when the imam is bowing, should he say the takbeers for starting to pray and for bowing, or say takbeer once and bow? 
He replied: 
It is better and more on the safe side to say takbeer twice, once for starting to pray, which is a pillar or essential part of the prayer which must be done when he is standing, and the second time for bowing when he starts to bow. If he fears that he may miss the rak’ah, then the opening takbeer will suffice according to the more correct of the two scholarly opinions, because they are two acts of worship being combined at the same time and the greater will suffice for the lesser. And this rak’ah will count according to the majority of scholars. End quote. 
Majmoo’ Fataawa Ibn Baaz, 11/244-245 
The one who is joining the prayer has to say the opening takbeer standing. If he says it whilst leaning forward to bow, it is not valid. 
Al-Nawawi said in al-Majmoo’ (4/111): 
If a person catches up with the imam when he is bowing, he should say the opening takbeer standing, then say the takbeer for bowing as he is leaning forward to bow. If he says some of the opening takbeer when he is not standing upright, then his prayer does not count as an obligatory prayer, with no difference of opinion among the scholars on this point; it also does not count as a naafil prayer, according to the correct view. End quote. 
See al-Mughni, 2/130 
Shaykh Ibn ‘Uthaymeen (may Allahhave mercy on him) said in al-Sharh al-Mumti’ (4/123): 
But there is a matter which must be discussed, which is that it is essential to say the opening takbeer when standing straight, before leaning forward, because if a person leans forward when saying the opening takbeer, he will have said the opening takbeer when he was not standing straight, and the opening takbeer must be said when standing straight. End quote. 
Thirdly: 
If he bows with the imam, that rak’ah counts for him even if he does not recite al-Faatihah. This is the view of the majority and it is the correct view, in sha Allah, because the Prophet (peace and blessings of Allahbe upon him) said to Abu Bakrah (may Allahbe pleased with him), when he came to the Prophet (peace and blessings of Allahbe upon him) when he was bowing and he bowed before he reached the row. He mentioned that to the Prophet (peace and blessings of Allahbe upon him) and he said: “May Allahmake you more keen, but do not do it again.” Narrated by al-Bukhaari, 783. 
The point here is that if catching up with bowing did not count as catching up with the rak’ah with the imam, the Prophet (peace and blessings of Allahbe upon him) would have told him to make up that rak’ah in which he did not catch up with the recitation, but no such thing has been reported from him. This indicates that the one who catches up with bowing has caught up with the rak’ah.
 See Silsilat al-Ahaadeeth al-Saheehah, p. 230. 
Al-Shawkaan said: Similarly the Prophet (peace and blessings of Allahbe upon him) told the one who joins the prayer to do what the imam does, and it is known that this cannot be done unless he bows with his imam. If he starts to recite al-Faatihah, he has caught up with the imam in a state where he is not doing what his imam does, so he has disobeyed the command to follow the imam. End quote from an essay quoted by the author of ‘Awn al-Ma’bood, 3/157 
With regard to the evidence for it being obligatory to recite al-Faatihah in prayer, this is general in meaning and includes the one who joins the prayer late and the one who does not join the prayer late. This hadeeth specifically indicates that the obligation to recite al-Faatihah is waived for the one who catches up with his imam when he is bowing, so this hadeeth makes an exception from the general meaning of the other ahaadeeth.  
See Majmoo’ al-Fataawa, 23/290 
In the answer to question no. 74999 we have explained that recitation of al-Faatihah is waived for the person praying behind an imam in two cases: 
1 – If he catches up with the imam when he is bowing
2 – If he catches up with the imam just before he bows, and he cannot complete the recitation of al-Faatihah 
See Ahkaam Hudoor al-Masaajid (p. 141-143) by Shaykh ‘Abd-Allahibn Saalih al-Fawzaan.