cosx-cos2x=2sin(3x/2)sin(x/2)求过程求解释
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cosx-cos2x=2sin(3x/2)sin(x/2)求过程求解释
cosx-cos2x=2sin(3x/2)sin(x/2)求过程求解释
cosx-cos2x=2sin(3x/2)sin(x/2)求过程求解释
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
2sin(3x/2)sin(x/2)=-(cos2x-cos(x))=cosx-cos2x
直接是积化和差的公式···
这个其实书上应该有的吧。
从右边到左边 2sin(x+x/2)sin(x-x/2)=2(sin^2(x)cos^2(x/2)-sin^2(x/2)cos^2(x))
然后化简就OK 使用sin^2(x/2)=1-cos^2(x/2)带入