1.sin40°（tan10°-根号3）2.sin10°分之1-cos10°分之根号33.tan70°cos10°（根号3tan20°-1）4.sin50°（1+根号3tan10°）5.sin50°（1+根号3tan10°）

1. sin40°(sin10°/cos10°-sin60°/cos60°) √3=tan60°=sin60°/cos60°
=sin40°*(sin10°cos60°-cos10°sin60°)/cos10°*cos60°
=-sin40°*sin50°/(cos10°*1/2)
=-2sin40°cos40°/cos10°
=-sin80°/cos10°=-1
2.1/sin10°-sin60°/cos10°cos60°
=(cos10°cos60°-sin10°sin60°)/(sin10°cos10°cos60°)
=cos70°/(sin10°cos10°cos60°)
=2cos70°/(sin20°*1/2)
=4cos70°/sin20°=4sin20°/sin20°=4
3. tan70°cos10°（根号3tan20°-1）
= tan70°cos10°[(sin60°sin20°/cos60°cos20°)-1]
=tan70°cos10°[(sin60°sin20°-cos60°cos20°)/cos60°cos20°]
=-tan70°cos10°*cos80°/cos60°cos20°
=-tan70°cos10°*sin20°/(1/2*cos20°)
=-tan70°2cos10°*sin20°/cos20°)
=-tan70°*tan20°
=-1
4.sin50°（1+根号3tan10°）
=sin50°(1+sin60°sin10°/cos60°cos10°)
=sin50°(sin60°sin10°+cos60°cos10°)/cos60°cos10°
=sin50°cos50°/cos60°cos10°
=2sin50°cos50°/cos10°
=sin100°/cos10°
=1

①sin40°(tan10°-根号3)=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...