化简sin^2asin^2b+cos^2acos^2b-1/2cos2acos2brt

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化简sin^2asin^2b+cos^2acos^2b-1/2cos2acos2brt

化简sin^2asin^2b+cos^2acos^2b-1/2cos2acos2brt
化简sin^2asin^2b+cos^2acos^2b-1/2cos2acos2b
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化简sin^2asin^2b+cos^2acos^2b-1/2cos2acos2brt
原式=sin²asin²b+cos²acos²b-1/2(cos²a-sin²a)(cos²b-sin²b)
=(2sin²asin²b+2cos²acos²b-cos²acos²b+cos²asin²b+sin²acos²b-sin²asin²b)/2
=(sin²asin²b+cos²acos²b+cos²asin²b+sin²acos²b)/2
=(sin²a+cos²a)(sin²b+cos²b)/2
=1/2

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sin^2asin^2b+cos^2acos^2b-1/2cos2acos2b
=(sinasinb+cosacosb)^2-2sinasinbcosacosb-1/2cos2acos2b
=cos^2(a-b)-1/2sin2asin2b-1/2cos2acos2b
=cos^2(a-b)-1/2(cos(2a-2b)
=1/2(cos(2a-2b)+1)-1/2(cos(2a-2b)
=1/2.