1/tan70度+4cos70度=

原式=cos70°/sin70°+ 4cos70°
=sin20°/cos20°+ 4sin20°
=(sin20°+4sin20°cos20°)/cos20°
=(sin20°+2sin40°)/cos20°
=[sin(30°-10°)+2sin(30°+10°)]/cos20°
=[sin30cos10-cos30sin10+2sin30cos10+2cos30sin10]/cos20°
=(3sin30cos10+cos30sin10)/cos20°
=根号3·(根号3/2cos10°+1/2sin10°)/cos20°【把sin30°和cos30°的值带入】
=根号3·(sin60cos10+cos60sin10)/cos20°
=根号3·sin(60+10)/cos20°
=根号3·sin70/cos20=根号3·cos20/cos20=根号3.
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