三角函数公式的问题cosx2-cosx1=-[2sin(x1+x2)/2]*[sin(x2-x1)/2]这个是怎么化出来啊?

Question

三角函数公式的问题
cosx2-cosx1=-[2sin(x1+x2)/2]*[sin(x2-x1)/2]
这个是怎么化出来啊?

Answer 1

把x2=a,x1=b吧,这样好看点.也就是cosa-cosb=-[2sin(a+b)/2]*[sin(a-b)/2]我们知道cos(x+y)=cosxcosy-sinxsinycos(x-y)=cosxcosy+sinxsiny把两式相减得cos(x+y)-cos(x-y)=cosxcosy-sinxsiny-cosxcosy-sinxsiny=-2sinx...