Answer
$$\cos(\theta-30^\circ)=\frac{\sqrt3\cos\theta+\sin\theta}{2}$$
Work Step by Step
$$X=\cos(\theta-30^\circ)$$
We apply the cosine difference identity, which states
$$\cos(A-B)=\cos A\cos B+\sin A\sin B$$
$$X=\cos\theta\cos30^\circ+\sin\theta\sin30^\circ$$
$$X=\cos\theta\times\frac{\sqrt3}{2}+\sin\theta\times\frac{1}{2}$$
$$X=\frac{\sqrt3\cos\theta+\sin\theta}{2}$$
Therefore, $$\cos(\theta-30^\circ)=\frac{\sqrt3\cos\theta+\sin\theta}{2}$$
