How would one approach finding this limit without using Taylor's series? $$\lim_{x \to 0} \frac{\tan{(\sin{(x)}})}{\sin{(\tan{(x)}})}$$
2026-04-13 08:57:29.1776070649
Limit of $\frac{\tan{(\sin{(x)}})}{\sin{(\tan{(x)}}}$ when x approaches 0
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HINT
By standard limits use that
$$\frac{\tan{(\sin{x}})}{\sin{(\tan{x}})} =\frac{\tan{(\sin{x}})}{\sin x} \frac{\tan x}{\sin{(\tan{x}})} \frac{\sin x}{x}\frac{x}{\tan x}$$