作业帮sin40(√3—tan10°) 要详细解题过程!
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 05:22:46
sin40(√3—tan10°) 要详细解题过程!
sin40(√3—tan10°) 要详细解题过程!
sin40(√3—tan10°) 要详细解题过程!
sin40°(√3-tan10°)
=sin40°sin10°/cos10°-√3sin40°
=sin40°cos80°/cos10°-√3sin40°
=-sin40°cos80°/2sin40°cos40°+√3sin40°
=-(1/2)cos80°/cos40°+√3sin40°
=-[(1/2)cos80°-√3sin40°sin40°]/cos40°
=-[(1/2)cos80°-√3/2sin80°]/cos40°
=-(sin30cos80°-cos30°sin80°)/cos40°
=-sin(30°-80°)/cos40°
=sin50°/cos40°
=1
sin40°(根号3-tan10°)
=sin40*sin10/cos10-根号3*sin40
=sin40*cos80/cos10-根号3*sin40
=-sin40*cos80/2sin40*cos40+根号3*sin40
=-(1/2)*cos80/cos40+根号3*sin40
=-[(1/2)*cos80-根号3sin40*sin40]/cos40...
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sin40°(根号3-tan10°)
=sin40*sin10/cos10-根号3*sin40
=sin40*cos80/cos10-根号3*sin40
=-sin40*cos80/2sin40*cos40+根号3*sin40
=-(1/2)*cos80/cos40+根号3*sin40
=-[(1/2)*cos80-根号3sin40*sin40]/cos40
=-[(1/2)cos80-根号3/2*sin80]/cos40
=-(sin30*cos80-cos30*sin80)/cos40
=-sin(30-80)/cos40
=sin50/cos40
=1
收起
sin40°(√3-tan10°)
=sin40°(tan60°-tan10°)
=sin40°sin(60°-10°)/(cos60°cos10°)
=sin40°cos40°/(1/2sin80°)
=1/2sin80°/(1/2sin80°)
=1
sin40°(√3-tan10°) =sin40°(√3-sin10°/cos10°) =sin40°(√3cos10°-sin10°)/cos10° =2sin40°(√3/2cos10°-1/2sin10°)/cos10° =2sin40°sin(60°-10°)/cos10° =2sin40°sin50°/cos10° =2sin40°cos40°/sin80° =sin80°/sin80° =1