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$$\lim \limits_{x \to \frac{\pi}{6}} \frac{\sin x-\sin \left(\frac{\pi}{6} \right)}{x-\frac{\pi}{6}}=$$

A

$-\cfrac{\sqrt{3}}{2}$

B

$-\cfrac{1}{2}$

C

$\cfrac{\sqrt{3}}{2}$

D

$\cfrac{1}{2}$

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