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### Limit $\lim_{x \to 0 }\frac{x}{\sin x} = 1$? [duplicate]

I have a question regarding limits. Recently in a math class, my teacher states that $\frac{\sin x}{x}$ goes to $1$ hence in the case of a $\lim_{x\to 0} \frac{x}{\sin x}$, the answer is $1$. Why is ...
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### Why is tangent of x greater than x? [duplicate]

I've seen the proof of $\lim_{x\rightarrow0} \frac{\sin(x)}{x}=1$ but it uses the fact that $\tan(x)>x$ which in all places says it is obvious but this is maths and a I'd like to see a purely ...
### Finding $\lim_{x\to 0}\frac{\sin x}{x}$ [duplicate]
How to find $$\lim_{x\to 0}\frac{\sin x}{x}$$
### Why does $\lim_{x\to0}\frac{\sin(x)}{x}$ equal $1$? [duplicate]
Without using L'Hospital's Rule, why does $$\lim_{x\to 0} \frac{\sin x}{x} = 1?$$