2022-01-06
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sinxsiny=1/2(cos(x-y)-cos(x+y))
令x=a,y=b
sinasinb=1/2(cos(a-b)-cos(a+b))
令x=a,y=b
sinasinb=1/2(cos(a-b)-cos(a+b))
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sinAsinB=sin[(A+B)/2+(A-B)/2]*sin[(A+B)/2-(A-B)/2]
=[sin(A+B)/2*cos(A-B)/2+cos(A+B)/2sin(A-B)/2]*[sin(A+B)/2*cos(A-B)/2-cos(A+B)/2sin(A-B)/2]
=[sin(A+B)/2*cos(A-B)/2]^2-[cos(A+B)/2sin(A-B)/2]^2
=[1-cos^2(A+B)/2]cos^2(A-B)/2-cos^2(A+B)/2sin^2(A-B)/2
=cos^2(A-B)/2-cos^2(A+B)/2[sin^2(A-B)/2+cos^2(A-B)/2]
=cos^2(A-B)/2-cos^2(A+B)/2
=1/2[1+cos(A-B)]-1/2[1+cos(A+B)]
=1/2[cos(A-B)-cos(A+B)]
=[sin(A+B)/2*cos(A-B)/2+cos(A+B)/2sin(A-B)/2]*[sin(A+B)/2*cos(A-B)/2-cos(A+B)/2sin(A-B)/2]
=[sin(A+B)/2*cos(A-B)/2]^2-[cos(A+B)/2sin(A-B)/2]^2
=[1-cos^2(A+B)/2]cos^2(A-B)/2-cos^2(A+B)/2sin^2(A-B)/2
=cos^2(A-B)/2-cos^2(A+B)/2[sin^2(A-B)/2+cos^2(A-B)/2]
=cos^2(A-B)/2-cos^2(A+B)/2
=1/2[1+cos(A-B)]-1/2[1+cos(A+B)]
=1/2[cos(A-B)-cos(A+B)]
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