Підготовка до ЗНО з математики. Алгебра.

$\begin{array}{l}\sin \alpha + \sin \beta = 2\sin \frac{{\alpha + \beta }}{2}\cos \frac{{\alpha - \beta }}{2};\\\sin \alpha - \sin \beta = 2\sin \frac{{\alpha - \beta }}{2}\cos \frac{{\alpha + \beta }}{2};\\\cos \alpha + \cos \beta = 2\cos \frac{{\alpha + \beta }}{2}\sin \frac{{\alpha - \beta }}{2};\\\cos \alpha - \cos \beta = - 2\sin \frac{{\alpha + \beta }}{2}\sin \frac{{\alpha - \beta }}{2};\\tg\,\alpha + tg\,\beta = \frac{{\sin (\alpha + \beta )}}{{\cos \alpha \cos \beta }},\alpha ,\beta \ne \frac{\pi }{2} + \pi n,n \in Z;\\tg\,\alpha - tg\,\beta = \frac{{\sin (\alpha - \beta )}}{{\cos \alpha \cos \beta }},\alpha ,\beta \ne \frac{\pi }{2} + \pi n,n \in Z;\\ctg\,\alpha + ctg\,\beta = \frac{{\sin (\alpha + \beta )}}{{\sin \alpha \sin \beta }},\alpha ,\beta \ne \pi n,n \in Z;\\ctg\,\alpha - ctg\,\beta = \frac{{ - \sin (\alpha - \beta )}}{{\sin \alpha \sin \beta }},\alpha ,\beta \ne \pi n,n \in Z.\end{array}$