[Math] Find the limit $\lim_{\theta\to 0} \frac{\sin \theta}{3\theta + \tan \theta}$

Question

Given problem
$$\lim_{\theta\to 0} \frac{\sin \theta}{3\theta + \tan \theta}$$

I got to
$$\lim_{\theta \to 0} \frac{\sin \theta \cos \theta}{3\theta \cos \theta + \sin \theta}$$

Now I'm lost. Any advice on how to be more efficient?

Answer 1

Hint : divide both side to $\theta $ and note that $$\lim _{ \theta \rightarrow 0 }{ \frac { \sin { \theta } }{ \theta } } =1\\ \lim _{ \theta \rightarrow 0 }{ \frac { \tan { \theta } }{ \theta } } =1\\ $$