Is it permissible to broadcast recorded Eid takbeers via the external loudspeakers of the mosque, while limiting the live takbeers of the worshippers to the inside of the mosque?

It is prescribed to recite the Takbir on the two Eids, individually and in congregations, using various wide-ranging formulas. It is recommended to raise one's voice with it in mosques, homes, and on roads, for both residents and travelers, due to its role in demonstrating the rituals of Islam. However, it is not appropriate to use recorded Takbir played through loudspeakers, because the obligation pertains to the worshippers themselves, and by doing so, they are deprived of the reward. This could also lead to people becoming lazy about reciting the Takbir or abandoning it altogether.