(Exaltation and Glorification of Allah)
The origin of Takbeer-e-Tashreek dates back to the time when Hazrat Ibraheem (Alayhis-Salaam) made Hazrat Ismaeel lie down. Allah Ta'ala ordered Hazrat Jibraiel (Alayhis-Salaam) to take along a ransom (fidyah) to the scene of the sacrifice of Hadrat Ismaeel (Alayhis-Salaam). When Hazrat Jibraeel (Alayhis-Salaam) appeared there, he feared Ibraheem (Alayhis- Salaam) would slaughter his son and thus began reciting,
Hearing his voice, Hazrat Ibraheem (Alayhis-Salaam) took to it as a glad tiding and exclaimed:
'Laa ilaha Illallahu wallaahu Akbar"
Hazrat Ismaeel (Alayhis-salaam) also thought that the fidyah had arrived and so he rose up to eulogize and thank Allah Ta'ala saying,
"Allahu Akbar wa Lillahil Hamd"
Allaahu Akbar, Allaahu Akbar. Laa ilaaha illallaahu wallaahu Akbar. Allaahu Akbar walillaahil hamd
Translation: "Allah is most great. Allah is most great. There is no Deity besides Allah and Allah is most Great. Allah is most Great and Verily all praises are for Allah."
It is waajib to recite this Takbeer audibly once after every Fard salaat from the morning of the ninth of Dhul Hijjah (Day of Arafah) till the Asr salaat of the thirteenth of Dhul Hijjah. The Fatwa is that the one that performs salaat with Jamaa'ah, and the one that performs it alone are the same as far as this law is concerned i.e. it is necessary to recite the Takbeer. It is waajib on both male and female. Females should not say the Takbeeraat loudly but softly. (Shami).
It is Mustahab (desirable) for those who read their salaat individually (men or women) and Musafirs (travellers) to recite these Takbeeraat softly.
Note: It is necessary for men to recite these Takbeeraat in a moderately loud voice. Many people are not mindful of this: either they read it softly or do not read it at all. This negligence should be remedied.
The Hadith background for Takbeer e Tashreeq can be found in the following Hadith of Muwatta Imam Malik
Yahya related to me from Malik from Yahya ibn Said that he had heard that on the day after the day of sacrifice Umar ibn al-Khattab went out a little after the sun had risen and said the takbir, and everyone repeated it after him. Then he went out a second time the same day when the sun was well up and said the takbir, and everyone repeated it after him. Then he went out a third time after mid-day and said the takbir, and everyone repeated it after him until it resounded from group to group until it reached the House and people knew that Umar had left to throw the stones. Malik said, "What we do here (in Madina) is to say the takbir during the days of tashriq after each prayer. The first time is when the imam and everyone with him says the takbir after the dhuhr prayer on the day of sacrifice, and the last is when the imam and everyone with him says the takbir after subh on the last of the days of tashriq, after which he stops saying the takbir." Malik said, "The takbirs during the days of tashriq should be done by both men and women, whether they are in a group or by themselves, at Mina or elsewhere, and all of the takbirs should be done. In this everyone follows the imam of the hajj and the people at Mina, because when everyone returns (to Makka) and comes out of ihram they keep the same people as imams while out of ihram (as they did when they were in ihram). Some one who is not doing hajj does not follow them except for the takbirs during the days of tashriq." Malik said, "The 'limited number of days' are the days of tashriq."