Question

sin（x+y）sin(x-y)=sin^2x-sin^2y

是证明题，写下过程哦，嘿嘿
我有点看不懂~~~~~~5555555555

Answer 1

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

Answer 2

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；