بسم الله الرحمن الرحيم
Q: If a person enters late into the Masjid and finds the Imaam has already began the rukoo’, does the person say the takbeer [Allahu Akbar] and go straight into rukoo’ or does he say the takbeer to start the prayer and then say another takbeer for going into rukoo’?
A: What is better and more encompassing is that he makes 2 takbeers [says “Allahu Akbar” twice]. The first is the takbeeratul Ihraam [i.e. the “Allahu Akbar” to enter into the prayer] and that is a pillar and he must do that whilst he stands at the beginning. The second is the takbeer for going into rukoo’ and he says that as he descends down into rukoo’.
If, however, he fears he may miss the raka’at by saying both takbeers [since the Imaam may be on the verge of rising from the rukoo’], then the first one [takbeeratul Ihraam for actually entering into the prayer and starting it] is sufficient in accordance to the correct opinion of the scholars on that issue. That is due to the fact that they are two worships that have come together in one time [i.e. the two takbeers one after the other, the first to start the prayer an the second to go into rukoo’] in that instance the greater worship suffices for the smaller one, hence the takbeer for entering into the prayer suffices for the takbeer of going into rukoo’ if missing the raka’at is feared.
[Based on Shaikh bin Baz’s رحمه الله response on the issue, Official Website]