Tranformarea produselor în sume

$$\begin{gathered} \sin a·\cos b=\frac{1}{2}\left[\sin (a+b)+\sin (a-b)\right] \\ \cos a·\cos b=\frac{1}{2}\left[\cos (a+b)+\cos (a-b)\right] \\ \sin a·\sin b=\frac{1}{2}\left[\cos (a-b)-\cos (a+b)\right]. \end{gathered}$$