已知(sinx)2-(siny)2=m求sin(x y)sin(x-y)
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已知(sinx)2-(siny)2=m求sin(x y)sin(x-y)
求sin(x+y)sin(x-y)
求sin(x+y)sin(x-y)
因为:
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
得:sinAsinB=[cos(A-B)-cos(A+B)]/2
将公式应用于本题
sin(x+y)sin(x-y)
=(cos2y-cos2x)/2
=(1-2sin²y-1+2sin²x)/2
=sin²x-sin²y
=m
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
得:sinAsinB=[cos(A-B)-cos(A+B)]/2
将公式应用于本题
sin(x+y)sin(x-y)
=(cos2y-cos2x)/2
=(1-2sin²y-1+2sin²x)/2
=sin²x-sin²y
=m
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