Решить: Lim (x->0) tg2x/sin5x

Решите задачу:

$\lim_{x \to 0} \frac{tg2x}{sin5x} = \lim_{x \to 0} \frac{sin2x}{cos2x\cdot sin5x} = \lim_{x \to 0} \frac{1}{cos2x}\cdot \lim_{x \to 0} \frac{sin2x\cdot 5x\cdot 2}{2x\cdot 5\cdot sin5x} = \\ \\ = 1\cdot \lim_{x \to 0} \frac{sin2x}{2x}\cdot \lim_{x \to 0} \frac{5x}{ sin5x}\cdot \lim_{x \to 0} \frac{2}{5}=1\cdot 1\cdot 1\cdot \frac{2}{5}= \frac{2}{5}$