Rewrite $\cos \left(x-\frac{5 \pi}{6}\right)$ in terms of $\sin (x)$ and $\cos (x)$. Question Help: Video Calculator Submit Question

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: \[\boxed{\cos \left(x-\frac{5 \pi}{6}\right) = \frac{1}{2}\sin(x) - \frac{\sqrt{3}}{2}\cos(x)}\]