sin(x+y)sin(x-y)=sin^2x-sin^2y
来源:百度知道 编辑:UC知道 时间:2024/05/27 03:03:16
是证明题,写下过程哦,嘿嘿
我有点看不懂~~~~~~5555555555
我有点看不懂~~~~~~5555555555
本题应用积化和差公式:
(先说说公式推导:
cos(x+y)=cosxcosy-sinxsiny;
cos(x-y)=cosxcosy+sinxsiny;
于是sinxsiny=(cos(x-y)-cos(x+y))/2;
)
将公式应用于本题
左边=sin(x+y)sin(x-y)=(cos2y-cos2x)/2
=(1-2sin^2y-1+2sin^2x)/2
=sin^2x-sin^2y=右边
所以命题得证;
sin(x+y)sin(x-y)
=1/2[COS(X+Y-X+Y)-COS(X+Y+X-Y)]
=1/2(COS2Y-COS2X)
=1/2(1-2SIN^2Y-1+2SIN^2X)
=SIN^X-SIN^2Y
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