Question

sin40(√3—tan10°) 要详细解题过程！！！！！！！！！！！！

Answer 1

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

追问

为什么sin50°/cos40°=1？

追答

sin50°=cos40°

追问

为什么sin50°=cos40°

追答

sin50°＝cos（90°-50°）＝cos40° 呀 公式

Answer 2

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

Answer 3

sin40°(√3-tan10°)
=sin40°(tan60°-tan10°)
=sin40°sin(60°-10°)/(cos60°cos10°)
=sin40°cos40°/(1/2sin80°)
=1/2sin80°/(1/2sin80°)
=1

Answer 4

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