求证cos(a+b)cos(a-b)=cos^2b-sin^2a

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求证cos(a+b)cos(a-b)=cos^2b-sin^2a

求证cos(a+b)cos(a-b)=cos^2b-sin^2a
求证cos(a+b)cos(a-b)=cos^2b-sin^2a

求证cos(a+b)cos(a-b)=cos^2b-sin^2a
cos(a+b)cos(a-b)
=(cosacosb-sinasinb)(cosacosb+sinasinb)
=(cosacosb)^2-(sinasinb)^2
=cos^2acos^2b-sin^2asin^2b
=cos^2acos^2b-(1-cos^2a)(1-cos^2b)
=cos^2acos^2b-(1-cos^2a-cos^2b+cos^2acos^2b)
=cos^2acos^2b-1+cos^2a+cos^2b-cos^2acos^2b
=-1+cos^2a+cos^2b
=-(cos^2a+sin^2a)+cos^2a+cos^2b
=-cos^2a-sin^2a+cos^2a+cos^2b
=cos^2b-sin^2a