if the formulas aren't rendered correctly,please refresh the web page \sin{\alpha}+\sin{\beta}=2\sin{\frac{\alpha+\beta}{2}}\cos{\frac{\alpha-\beta}{2}}\\ \sin{\alpha}-\sin{\beta}=2\cos{\frac{\alpha+\beta}{2}}\sin{\frac{\alpha-\beta}{2}}\\ \cos{\alpha}+\cos{\beta}=2\cos{\frac{\alpha+\beta}{2}}\cos{\frac{\alpha-\beta}{2}}\\ \cos{\alpha}-\cos{\beta}=-2\sin{\frac{\alpha+\beta}{2}}\sin{\frac{\alpha-\beta}{2}}\\ \sin{\alpha}\cos{\beta}=\frac{\sin{(\alpha+\beta)}+\sin{(\alpha-\beta)}}{2}\\ \cos{\alpha}\sin{\beta}=\frac{\sin{(\alpha+\beta)}-\sin{(\alpha-\beta)}}{2}\\ \cos{\alpha}\cos{\beta}=\frac{\cos{(\alpha+\beta)}+\cos{(\alpha-\beta)}}{2}\\ \sin{\alpha}\sin{\beta}=\frac{\cos{(\alpha+\beta)}-\cos{(\alpha-\beta)}}{2}\\