Question

cosx-cos2x=2sin(3x/2)sin(x/2)求过程求解释

Answer 1

和差化积公式

cos α-cos β=-2sin[(α+β)/2]·sin[(α-β)/2]

推导过程：

cos(a+b)=cosacosb-sinasinb

cos(a-b)=cosacosb+sinasinb

上面两式相减,得：

cos(a+b)-cos(a-b)=-2sinasinb

令a+b=x a-b=y 则a=(x+y)/2 b=(x-y)/2

cosx-cosy=-2sin(x+y)/2*sin(x-y)/2