sin^220°+cos^250°+sin30°sin70°

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sin^220°+cos^250°+sin30°sin70°sin^220°+cos^250°+sin30°sin70°sin^220°+cos^250°+sin30°sin70°(sin20)^2+

sin^220°+cos^250°+sin30°sin70°
sin^220°+cos^250°+sin30°sin70°

sin^220°+cos^250°+sin30°sin70°
(sin20)^2+(cos50)^2+sin30*sin70
=(sin20)^2+(cos50)^2+sin(50-20)*sin(50+20)
=(sin20)^2+(cos50)^2+(sin50cos20-cos50sin20)*(sin50cos20+cos50sin20)
=(sin20)^2+(cos50)^2+(sin50)^2*(cos20)^2-(cos50)^2*(sin20)^2
=(sin20)^2*[1-(cos50)^2]+(cos50)^2+(sin50)^2*(cos20)^2
=(sin20)^2*(sin50)^2+(cos50)^2+(sin50)^2*(cos20)^2
=(sin50)^2*[(sin20)^2+(cos20)^2]+(cos50)^2
=(sin50)^2+(cos50)^2
=1

约等于:0.117+0.117+0.4698≈0.7038