\(\tan (A \pm B)=\frac{\tan A \pm \tan B}{1 \mp\tan A \tan B}\\ \sin A + \sin B = 2 \sin \frac{1}{2}(A+B)\cos \frac{1}{2}(A – B)\\ \sin A – \sin B = 2 \cos \frac{1}{2}(A+B)\sin \frac{1}{2} (A – B)\\ \cos A + \cos B = 2 \cos \frac{1}{2}(A+B)\cos \frac{1}{2} (A – B)\\ \cos A - \cos B = 2 \sin \frac{1}{2}(A+B)\sin \frac{1}{2} (A – B)\\ \)