Should one who joins the prayer late recite the opening du‘aa’?
Question

                The opening du‘aa’ (du‘aa’ al-istiftaah) should come at the beginning of the prayer. If I join the congregation at the beginning of the second rak‘ah, for example, should I recite it or have I missed the time for it? In other words, should the opening du‘aa’ be recited only in the first rak‘ah, and after that should it not be recited? Or is it that whenever the worshipper starts his prayer, he should say it even if he did not say it in the first rak‘ah?
Praise be to Allah.
    The opening du‘aa’ 
    is Sunnah according to the majority of scholars, and whenever the worshipper 
    catches up with his imam in the first or second rak‘ah, he should recite the 
    opening du‘aa’, so long as he is not worried that the imam will bow (too 
    soon). But if he is worried that the imam will bow, then he should recite 
    al-Faatihah only, because reciting it is obligatory. 

    An-Nawawi (may 
    Allah have mercy on him) said: If one who joins the prayer late starts to 
    pray, then the imam says Ameen immediately after he has started to pray, 
    then he should say Ameen and then recite the opening du‘aa’, because the 
    saying ameen is brief. If the one who joins the prayer late catches up with 
    the imam in the final tashahhud, he should say takbeer and sit down, then if 
    the imam says the salaam as soon as he has sat down, then he should stand up 
    (to make up what he has missed of the prayer) and not say the opening 
    du‘aa’, because he has missed the place for it.

    End quote from 
    al-Majmoo‘, 3/275 

    He also said: If 
    he catches up with him when he is still standing, and he knows that he will 
    be able to recite the opening du‘aa’ and seek refuge with Allah and recite 
    al-Faatihah, then he must do so. This was stated by ash-Shaafa‘i in 
    al-Umm, and also by our companions. … If he knows that he will only be 
    able to recite part of the opening du‘aa’ and seek refuge with Allah and 
    recite al-Faatihah, and he will not be able to do all of it, he should do 
    what he is able to do. This was stated in al-Umm.

    End quote from 
    al-Majmoo‘, 3/276 

    Shaykh ‘Abd 
    al-‘Azeez (may Allah have mercy on him) said: 

    If the latecomer 
    joins the prayer when the imam is reaching the end of his recitation, before 
    bowing, should he start his prayer with the opening du‘aa’, or should he 
    join the imam and remain silent? 

    He replied: 

    If the latecomer 
    arrives when the imam is bowing, he should bow with him, and not recite the 
    opening du‘aa’ or recite any Qur’an; rather he should say takbeer and bow. 
    But if he comes when the imam is still standing and there is plenty of time, 
    then he should recite the opening du‘aa’ and al-Faatihah. This is what is 
    prescribed for him: to recite the opening du‘aa’ and then al-Faatihah, even 
    in the prayers in which the imam recites out loud. If there is a pause where 
    the imam falls silent, he should recite it at that time; otherwise he should 
    recite it to himself, then after that he should listen attentively to the 
    imam. But if he comes late, when the imam is bowing, then he should say 
    takbeer and bow, and the requirement to recite al-Faatihah is waived in this 
    case, because he is excused. 

    End quote from 
    Majmoo‘ al-Fataawa, 30/150 

    And Allah knows 
    best.