[Math] Limit of the greatest integer of $\frac{100 \tan(x) \sin(x)}{x^2}$ as $x$ tends to $0$

Question

$$\lim_{x \to 0} \left[ \frac{100 \tan(x) \sin (x)}{x^2} \right],$$ where $\left[ \phantom{\frac{1}{1}} \right]$ denotes the greatest integer (floor) function.

I am having problem as $\frac{\sin(x)}{x}$ is always less than $1$ and $\frac{\tan(x)}{x}$ is always greater than $1.$

Answer 1

write it in the form $$100\frac{\sin(x)}{x}\frac{1}{\cos(x)}\frac{\sin(x)}{x}$$ can you proceed?