Answer
$$\cos(60^\circ+\theta)=\frac{\cos\theta-\sqrt3\sin\theta}{2}$$
Work Step by Step
$$X=\cos(60^\circ+\theta)$$
To expand the formula, cosine sum identity would be used:
$$\cos(A+B)=\cos A\cos B-\sin A\sin B$$
That means
$$X=\cos60^\circ\cos\theta-\sin60^\circ\sin\theta$$
$$X=\frac{1}{2}\cos\theta-\frac{\sqrt3}{2}\sin\theta$$
$$X=\frac{\cos\theta-\sqrt3\sin\theta}{2}$$
Therefore, $$\cos(60^\circ+\theta)=\frac{\cos\theta-\sqrt3\sin\theta}{2}$$
