证明sin(A+B)sin(A-B)=cos^2B-cos^2A
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证明sin(A+B)sin(A-B)=cos^2B-cos^2A
![证明sin(A+B)sin(A-B)=cos^2B-cos^2A](/uploads/image/z/16044652-28-2.jpg?t=%E8%AF%81%E6%98%8Esin%28A%2BB%29sin%28A-B%29%3Dcos%5E2B-cos%5E2A)
sin(a+b)sin(a-b)
=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin^2acos^2b-cos^2asin^2b
=(1-cos^2a)cos^2b-cos^2a(1-cos^2b)
=cos^2b-cos^2acos^2b-cos^2a+cos^2acos^2b
=cos^2b-cos^2a
=(sinacosb+cosasinb)(sinacosb-cosasinb)
=sin^2acos^2b-cos^2asin^2b
=(1-cos^2a)cos^2b-cos^2a(1-cos^2b)
=cos^2b-cos^2acos^2b-cos^2a+cos^2acos^2b
=cos^2b-cos^2a
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