If the Rav of the shul or yeshiva made a mistake and started saying Tachanun on a day of no Tachanun, should one pretend to say it to avoid embarrassing him?

Horav Shlomo Miller’s Shlit’a opinion is that one should not directly correct the Rov as that likely will be embarrassing and most likely also done in public. One may quietly ask as a question if Tachanun is recited on that day.