Transformarea sumelor în produse

$$\begin{gathered} \sin a+\sin b=2\sin \frac{a+b}{2}\cos \frac{a-b}{2} \\ \sin a-\sin b=2\sin \frac{a-b}{2}\cos \frac{a+b}{2} \\ \cos a+\cos b=2\cos \frac{a+b}{2}\cos \frac{a-b}{2} \\ \cos a-\cos b=-2\sin \frac{a+b}{2}\sin \frac{a-b}{2} \\ tga+tgb=\frac{\sin (a+b)}{\cos a·\cos b}, \cos a\ne 0, \cos b\ne 0 \\ tga-tgb=\frac{\sin (a-b)}{\cos a·\cos b}, \cos a\ne 0, \cos b\ne 0. \end{gathered}$$