sin(a+b)=sinacosb+cosasinbsin(a-b)=sinacosb-cosasinb两式相加得：sinacosb=1/2[sin(a+b)+sin(a-b)]...(1)两式相减得：cosasinb=1/2[sin(a+b)-sin(a-b)]...(2)cos(a+b)=cosacosb-sinasinbcos(a-b)=cosacosb+sinasinb两式相加得：cosacosb=1/2[cos(a+b)+cos(a-b)]...(3)两式相减得：sinasinb=-1/2[cos(a+b)-cos(a-b)]...(4)用(a+b)/2、(a-b)/2分别代替上面四式中的a,b就可得到和差化积的四个式子.如：(1)式可变为：sina+sinb=2sin[(a+b)/2]*cos[(a-b)/2]其它依次类推即可.