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