$ \sin(x) \simeq \tan(x) $ when $ x \rightarrow 0 $ - Maclaurin series

Question

I'm wondering if it is correct to say that:

$$ \sin(x) \simeq \tan(x) \quad \text{when} \quad x \rightarrow 0 $$

because, according to Maclaurin series:

$$ \sin(x) \simeq x \quad \text{when} \quad x \rightarrow 0 $$

and

$$ \tan(x) \simeq x \quad \text{when} \quad x \rightarrow 0 $$

Thank you in advance.

Answer 1

Since $\frac{\sin x}{\tan x}=\cos x\to1$ as $x\to0$, $\sin x\sim\tan x$ (sources differ on whether to use $\sim$ or $\simeq$).