Ta có:
\(\begin{array}{l}\cos \alpha \cos \beta = \cos \frac{{\alpha + \beta }}{2}\cos \frac{{\alpha - \beta }}{2}\\ = \frac{1}{2}\left[ {\cos \left( {\frac{{\alpha + \beta }}{2} + \frac{{\alpha - \beta }}{2}} \right) + \cos \left( {\frac{{\alpha + \beta }}{2} - \frac{{\alpha - \beta }}{2}} \right)} \right]\\ = \frac{1}{2}\left( {\cos \alpha + \cos \beta } \right)\end{array}\)
\(\begin{array}{l}\sin \alpha \sin \beta = \sin \frac{{\alpha + \beta }}{2}\sin \frac{{\alpha - \beta }}{2}\\ = \frac{1}{2}\left[ {\cos \left( {\frac{{\alpha + \beta }}{2} - \frac{{\alpha - \beta }}{2}} \right) - \cos \left( {\frac{{\alpha + \beta }}{2} + \frac{{\alpha - \beta }}{2}} \right)} \right]\\ = \frac{1}{2}\left( {\cos \beta - \cos \alpha } \right)\end{array}\)
\(\begin{array}{l}\sin \alpha \cos \beta = \sin \frac{{\alpha + \beta }}{2}\cos \frac{{\alpha - \beta }}{2}\\ = \frac{1}{2}\left[ {\sin \left( {\frac{{\alpha + \beta }}{2} + \frac{{\alpha - \beta }}{2}} \right) + \sin \left( {\frac{{\alpha + \beta }}{2} - \frac{{\alpha - \beta }}{2}} \right)} \right]\\ = \frac{1}{2}\left( {\sin \alpha + \sin \beta } \right)\end{array}\)
