#### Answer

$\frac{\cos\theta-\sqrt{3}\sin\theta}{2}$

#### Work Step by Step

Use the addition formula for cosine, $\cos (A+B)=\cos A\cos B-\sin A\sin B$:
$\cos(60^\circ+\theta)$
$=\cos 60^\circ\cos \theta-\sin 60^\circ\sin \theta$
$=\frac{1}{2}*\cos\theta-\frac{\sqrt{3}}{2}*\sin\theta$
$=\frac{\cos\theta}{2}-\frac{\sqrt{3}\sin\theta}{2}$
$=\frac{\cos\theta-\sqrt{3}\sin\theta}{2}$