Question

高一数学题！在线等！急急急！有步骤！

化简cos(x加y)cos(x减y)减sin(x加y)sin(x减y)，答案是cos2x，求步骤！

Answer 1

用余弦的和角公式即可：cos(x+y)cos(x-y)-sin(x+y)sin(x-y)=cos[(x+y)+ (x-y)]=cos2x

Answer 2

cos(x+y)cos(x-y)-sin(x+y)sin(x-y)
=(cosxcosy-sinxsiny)(cosxcosy+sinxsiny)-(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)
=(cos^2 xcos^2 y-sin^2 xsin^2 y)-(sin^2 xcos^2 y-cos^2 xsin^2y)
=cos^2 xcos^2 y-sin^2 xsin^2 y-sin^2 xcos^2 y+cos^2 xsin^2y
=(cos^2 xcos^2 y+cos^2 xsin^2y)-sin^2 xsin^2 y-sin^2 xcos^2 y
=(cos^2 xcos^2 y+cos^2 xsin^2y)-(sin^2 xsin^2 y+sin^2 xcos^2 y)
=cos^2 x(cos^2y+sin^2y)-sin^2x(sin^2y+cos^2y)
=cos^2x-sin^2x
=cos2x

Answer 3

cos(x+y)cos(x-y)-sin(x+y)sin(x-y)=cos[(x+y)+(x-y)]=cox2x

Answer 4

cosacosb-sinasinb=cos(a+b),a=x+y,b=x-y
cos(x+y)cos(x-y)-sin(x+y)sin(x-y)=cos(x+y+x-y)=cos(2x)

Answer 5

由定理cos(A+B)=cosAcosB-sinAsinB
得cos(x+y)cos(x-y)-sin(x+y)sin(x-y)=cos((x+y)+(x-y))=cos2x