求证:sin^2acos^2b-cos^2asin^2b=cos^2b-cos^2a

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求证:sin^2acos^2b-cos^2asin^2b=cos^2b-cos^2a
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求证:sin^2acos^2b-cos^2asin^2b=cos^2b-cos^2a
求证:sin^2acos^2b-cos^2asin^2b=cos^2b-cos^2a

求证:sin^2acos^2b-cos^2asin^2b=cos^2b-cos^2a
证明:
左边=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
右边=cos^2b-cos^2a
左边=右边
所以sin^2acos^2b-cos^2asin^2b=cos^2b-cos^2a