(sinx+siny)^2+(cosx+cosy)^2为什么等于1+1+2(sinxsiny+cosxcosy)=2+2cos(x-y)

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(sinx+siny)^2+(cosx+cosy)^2为什么等于1+1+2(sinxsiny+cosxcosy)=2+2cos(x-y)
(sinx+siny)^2+(cosx+cosy)^2为什么等于1+1+2(sinxsiny+cosxcosy)=2+2cos(x-y)

(sinx+siny)^2+(cosx+cosy)^2为什么等于1+1+2(sinxsiny+cosxcosy)=2+2cos(x-y)
(sinx+siny)^2+(cosx+cosy)^2
= sinx^2 + siny^2 + 2sinxsiny + cosx^2 + cosy^2 + 2cosxcosy
=（sinx^2 + cosx^2）+（siny^2 + cosy^2）+ 2sinxsiny + 2cosxcosy
= 1 + 1 + 2 (sinxsiny + cosxcosy）
再根据 余弦差交公式 sinxsiny+cosxcosy = cos（x-y）
即得 （sinx+siny)^2+(cosx+cosy)^2
= 1 + 1 + 2 (sinxsiny + cosxcosy)
= 2 + 2cos(x-y)

(sinx+siny)^2+(cosx+cosy)^2
=(sinx)^2+2sinxsiny+(siny)^2+(cosx)^2+2cosxcosy+(cosy)^2
=(sinx)^2+(cosx)^2+(siny)^2+(cosy)^2+2sinxsiny+2cosxcosy
=1+1++2(sinxsiny+cosxcosy) [公式(sinx)^2+(cosx)^2=1]
=2+2cos(x-y) [公式cos(x-y)=cosxcosy+sinxsiny]

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