Past life (18~24) of louwang: 數學

積化和差:

$sin\alpha*cos\beta=\frac{1}{2}(sin(\alpha+\beta)+sin(\alpha-\beta))$

$cos\alpha*sin\beta=\frac{1}{2}(sin(\alpha+\beta)-sin(\alpha-\beta))$

$cos\alpha*cos\beta=\frac{1}{2}(cos(\alpha+\beta)+cos(\alpha-\beta))$

$sin\alpha*sin\beta=\frac{-1}{2}(cos(\alpha+\beta)-cos(\alpha-\beta))$

和差化積:

$sin\alpha+sin\beta=2sin\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2}$

$sin\alpha-sin\beta=2cos\frac{\alpha+\beta}{2}sin\frac{\alpha-\beta}{2}$

$cos\alpha+cos\beta=2cos\frac{\alpha+\beta}{2}cos\frac{\alpha-\beta}{2}$

$cos\alpha-cos\beta=-2sin\frac{\alpha+\beta}{2}sin\frac{\alpha-\beta}{2}$

Past life (18~24) of louwang