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

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/09 17:26:51
(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]

(sinx-siny)(sinx+siny)-(cosx+cosy)(cosx-cosy)等於? 证明.（sinx+siny)/cosx-cosy=ctg(y-x)/2 sinx+siny=1/3,则siny-(cosx)^2的最大值为?最小值为? 已知sinx+siny=1/3求siny-(cosx)^2的最小值和最大值 已知sinx+siny=1/3求siny-(cosx)^2的最小值 证明cosx(cosx-cosy)+sinx(sinx-siny)=2sin(x-y)/2 已知sinx+siny=2/3cosx+cosy=2/3,则sinx+cosx的值? 求y=(sinx)^2-cosx+2最值已知sinx+siny=1/3,求siny-(cosx)^2的最值 sinx+siny=2/5,cosx+cosy=6/5,求cos(2x-2y) 若cosx*cosy+sinx*siny=1/3 ,则cos(2x-2y)=? 已知sinx+cosy=根号2/2,求t=cosx+siny的取值范围? sinx+siny=2分之根号2求cosx+cosy的范围 sinx+siny=√2/2,求cosx+cosy的取值范围 sinx+siny=√2/2 则cosx+cosy的取值范围是 sinx+siny=根号(2)/2,则cosx+cosy的取值范围? 已知sinx+siny=根号2/2求cosx+cosy的取值范围 已知sinx+siny=√2,cosx+cosy=2√3/3,求tanx*tany 已知cosx+cosy=1/2,sinx-siny=1/3,求cos(x+y)