cos2αcos2β-cos^2(α-β)
=cos2αcos2β-1/2[1+co2(α-β)]
=cos2αcos2β-1/2[1+cos2αcos2β+sin2αsin2β]
=-1/2+1/2[cos2αcos2β-sin2αsin2β]
=-1/2+1/2cos2(α+β)
=-1/2+1/2[(1-tan²(α+β)/(1+tan²(α+β)]
因为
tan(α+β)/2=1/2
所以
tan(α+β)=2tan[(α+β)/2]/(1-tan²[(α+β)/2])=1/[1-1/4]=4/3
所以
原式=-1/2+1/2[(-7/9)/25/9]
=-1/2-7/50
=-16/25