Netanyahu is neither religious nor sincere. He probably has to show up at the synagogue on Rosh Hashanah, or else it will look bad to his many traditional Mizrahim supporters. He will probably mouth the prayers that are read aloud so he looks OK. But there is one line in the Avinu Malkenu prayer that he will be sincere about: "Our father and King, in thy mercy, delete all of our debt notes. = אָבִינוּ מַלְכֵּנוּ מְחֹק בְּרַחֲמֶיךָ הָרַבִּים כָּל שִׁטְרַי חוֹבוֹתֵינוּ." What can you do, the man doesn't like paying his own expenses, and when people give him a "service", he believes it is free of charge. So this prayer line he will recite sincerely so he does not get into legal hot water has happened in the past.
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from the article: Palestine, the UN, and lies at Rosh Hashanah