sin²20°＋cos²50°＋sin20°cos50°＝＿＿? 能告诉我过程吗?

sin²20°＋cos²50°＋sin20°cos50°＝＿＿? 能告诉我过程吗?
sin²20°＋cos²50°＋sin20°cos50°＝＿＿? 能告诉我过程吗?

sin²20°＋cos²50°＋sin20°cos50°＝＿＿? 能告诉我过程吗?
sin²20°+cos²50°+sin20°cos50°
=(1-cos40°)/2+(1+cos100°)/2+(1/2)*(sin70°-sin30°)
=(1-cos40°)/2+(1-cos80°)/2+(1/2)*(cos20°-1/2)
=1-(1/2)*(cos40°+cos80°)+(1/2)*(cos20°-1/2)
=1-(cos60°cos20°)+(1/2)cos20°-1/4
=1-(1/2)cos20°+(1/2)cos20°-1/4
=3/4;
sin²20°+cos²50°+sin20°cos50°
=(sin20°+cos50°)^2-sin20°cos50°
=(sin20°+sin40°)^2-sin20°cos50°
=(2sin30cos10)^2-sin20°cos50°
=(cos10°)^2--[sin70-sin30]/2
=(1+cos20°)/2 -[cos20°-1/2]/2
=3/4;

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