sinx=1/2 siny=1/3 ,sin(x+y)(sinx-y)=?数学达人帮我啊·······

来源：学生作业帮助网编辑：六六作业网时间：2024/11/27 14:44:59

sinx=1/2siny=1/3,sin(x+y)(sinx-y)=?数学达人帮我啊·······sinx=1/2siny=1/3,sin(x+y)(sinx-y)=?数学达人帮我啊·······si

sinx=1/2 siny=1/3 ,sin(x+y)(sinx-y)=?数学达人帮我啊·······
sinx=1/2 siny=1/3 ,sin(x+y)(sinx-y)=?
数学达人帮我啊·······

sinx=1/2 siny=1/3 ,sin(x+y)(sinx-y)=?数学达人帮我啊·······
sin(x+y)sin(x-y)=[sinxcosy+cosxsiny][sinxcosy-cosxsiny]
=(sinxcosy)^2-(cosxsiny)^2
=(sinx)^2[1-(siny)^2]-[1-(sinx)^2](siny)^2
=1/4*(1-1/9)-(1-1/4)*1/9
=5/36

用积化和差公式：
sin(x+y)*sin(x-y)=cos(2y)-cos(2x)=1-2siny^2+(1-2sinx^2)=2-2(1/4+1/9)=23/18

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