[tex]\tan(-x)=-\tan(x)\\\\\cos(-x)=\cos(x)\\\\\tan(x)=\dfrac{\sin(x)}{\cos(x)}\\\\\tan(-x)=-\dfrac{\sqrt7}{3}\to-\tan(x)=-\dfrac{\sqrt7}{3}\to\tan(x)=\dfrac{\sqrt7}{3}\\\\\sin(x):\tan(x)=\sin(x):\dfrac{\sin(x)}{\cos(x)}=\sin(x)\cdot\dfrac{\cos(x)}{\sin(x)}=\cos(x)\\\\\cos(x)=\sin(x):\tan(x)\to\cos(x)=\dfrac{\sqrt7}{4}:\dfrac{\sqrt7}{3}=\dfrac{\sqrt7}{4}\cdot\dfrac{3}{\sqrt7}=\dfrac{3}{4}\\\\Answer:\ \boxed{c.\ \dfrac{3}{4}}[/tex]
