Question

Evaluate on lim x->0 (1-cosx) / x sinx

Answer 1

`\lim_(x \to 0) (1-cos(x))/(xsin(x)) \\ \\ \lim_(x \to 0) (1-cos(x))/(x) (1)/(sin(x)) \\ \\\lim_(x \to 0) (1-cos(x))/(x^2) (x)/(sin(x)) \\ \\\lim_(x \to 0) (1-cos(x))/(x^2) (1)/((sin(x))/(x)) \\ \\\lim_(x \to 0) (1-cos(x))/(x^2) \lim_(x \to 0) (1)/((sin(x))/(x)) \\ \\\lim_(x \to 0) (1-cos(x))/(x^2) (1)/(\lim_(x \to 0)(sin(x))/(x)) \\ \\ (1)/(2) * (1)/(1) = (1)/(2)`