Rewrite $\cos \left(x-\frac{5 \pi}{6}\right)$ in terms of $\sin (x)$ and $\cos (x)$.
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Final Answer: \[\boxed{\cos \left(x-\frac{5 \pi}{6}\right) = \frac{1}{2}\sin(x) - \frac{\sqrt{3}}{2}\cos(x)}\]
Step 1 :The given expression is a cosine of a difference between two angles. We can use the cosine difference identity to rewrite the expression. The cosine difference identity is given by: \[\cos(a - b) = \cos(a)\cos(b) + \sin(a)\sin(b)\]
Step 2 :In this case, \(a = x\) and \(b = \frac{5\pi}{6}\). We know that \(\cos\left(\frac{5\pi}{6}\right) = -\frac{\sqrt{3}}{2}\) and \(\sin\left(\frac{5\pi}{6}\right) = \frac{1}{2}\). We can substitute these values into the identity to rewrite the expression in terms of \(\sin(x)\) and \(\cos(x)\).
Step 3 :Final Answer: \[\boxed{\cos \left(x-\frac{5 \pi}{6}\right) = \frac{1}{2}\sin(x) - \frac{\sqrt{3}}{2}\cos(x)}\]