cosxcosy=[cos(x+y)+cos(x-y)]/2 这个公式怎么证明？？？

这是中学的三角问题，但我忘了证明的方法，请指教。谢谢。

可以把等号从右向左证明的

其实右边的那两个余弦都可以拆开成两个部分，这样互相抵消一部分就成了左边的式子cosxcosy=1/2[(cosxcosy-sinxsiny)+(cosxcosy+sinxsiny)]

=[cos(x+y)+cos(x-y)]1/2

cos(x+y)=cosxcosy-sinxsiny

cos(x-y)=cosxcosy+sinxsiny

cos(x+y)=cosxcosy-sinxsiny

[cos(x+y)+cos(x-y)]/2=[cosxcosy-sinxsiny+cosxcosy+sinxsiny]/2=cosxcosy

cos(x+y)=cosxcosy-sinxsiny

cos(x-y)=cosxcosy+sinxsiny

[cos(x+y)+cos(x-y)]/2

=(cosxcosy-sinxsiny+cosxcosy+sinxsiny)/2

=cosxcosy

1/2[cos(x+y)+cos(x-y)]=1/2(cosxcosy -sinxsiny+cosxcosy+sinxsiny)

=cosxcosy