## Trigonometry (11th Edition) Clone

$$\cos(30^\circ+\theta)=\frac{\sqrt3\cos\theta-\sin\theta}{2}$$
$$X=\cos(30^\circ+\theta)$$ 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, $$\cos(30^\circ+\theta)=\frac{\sqrt3\cos\theta-\sin\theta}{2}$$