Rewrite as lim(x→0) [(10^sinx - 1)/sinx] · [sinx/tanx]. The first part lim(x→0) (10^sinx - 1)/sinx = ln 10 (using lim(u→0) (a^u - 1)/u = ln a). The second part sinx/tanx = cosx → 1. Therefore the limit equals ln 10.
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