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If the $\sin(x)$ is less than zero and $\tan(x)=2$, then find $\cos(x)$.

A

$\cfrac{1}{2}$

B

$\cfrac{1}{5}$

C

$-\cfrac{\sqrt{5}}{5}$

D

$\cfrac{\sqrt{5}}{5}$

E

$-\cfrac{2\sqrt{5}}{5}$

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