根据积化和差公式:sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
sin(a+b)sin(b-a)=1/2[cos(a+b+a-b)-cos(a+b-a-b)]
=1/2(cos2a-cos2b)
=1/2[(2cos^2a-1)-(2cos^2b-1)]
=1/2(2cos^2a-2cos^2b)
=1/2[2(cos^2a-cos^2b)]
=(cos^2a-cos^2b)
所以cos^2a-cos^2b=m
根据积化和差公式:sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
sin(a+b)sin(b-a)=1/2[cos(a+b+a-b)-cos(a+b-a-b)]
=1/2(cos2a-cos2b)
=1/2[(2cos^2a-1)-(2cos^2b-1)]
=1/2(2cos^2a-2cos^2b)
=1/2[2(cos^2a-cos^2b)]
=(cos^2a-cos^2b)
所以cos^2a-cos^2b=m