積\(\to\)和の公式
- \(\sin\alpha\cos\beta= \displaystyle\frac{1}{2} \left\{ \sin(\alpha+\beta)+\sin(\alpha-\beta) \right\} \)
- \(\cos\alpha\sin\beta= \displaystyle\frac{1}{2} \left\{ \sin(\alpha+\beta)-\sin(\alpha-\beta) \right\} \)
- \(\cos\alpha\cos\beta= \displaystyle\frac{1}{2} \left\{ \cos(\alpha+\beta)+\cos(\alpha-\beta) \right\} \)
- \(\sin\alpha\sin\beta= -\displaystyle\frac{1}{2} \left\{ \cos(\alpha+\beta)-\cos(\alpha-\beta) \right\} \)
和\(\to\)積の公式
- \( \sin A+\sin B = \displaystyle2\sin\frac{A+B}{2}\cos\frac{A-B}{2} \)
- \( \sin A-\sin B = \displaystyle2\cos\frac{A+B}{2}\sin\frac{A-B}{2} \)
- \( \cos A+\cos B = \displaystyle2\cos\frac{A+B}{2}\cos\frac{A-B}{2} \)
- \( \cos A-\cos B = \displaystyle-2\sin\frac{A+B}{2}\sin\frac{A-B}{2} \)
