化简求值：2cosˆ210°-tan5°（1+cos10°）-2sin40°sin80°

化简求值：2cosˆ210°-tan5°（1+cos10°）-2sin40°sin80°
化简求值：2cosˆ210°-tan5°（1+cos10°）-2sin40°sin80°

化简求值：2cosˆ210°-tan5°（1+cos10°）-2sin40°sin80°
2(cos10°)^2-tan5°（1+cos10°）-2sin40°sin80°
=cos20°+1-sin5°/cos5°*(1+2(cos5°)^2-1)-(cos(40°-80°)-cos(40°+80°))
=cos20°+1-2sin5°*cos5°-cos40°+cos120°
=cos20°-sin10°-cos40°+1/2
=cos20°-(cos80°+cos40°)+1/2
=cos20°-2*cos(60°)*cos20°+1/2
=cos20°-cos20°+1/2
=1/2
利用了正余弦的二倍角公式、积化和差、和差化积公式.