(1).=(cos10°-根号3*sin10°)/(sin10°cos10°)=4sin(30°-10°)/sin20°=4
(2)=sin40°(tan10°-根号3)=sin40°(sin10°/cos10°-根号3)
=sin40°(sin10°-根号3cos10°)/cos10°=2sin40°sin(10°-60°)/cos10°
=-2sin40°cos40°/cos10°=-sin80°/sin80°=-1
(3)=tan70°*cos10°*(√3 *tan20° -1)=tan70°*cos10°*(tan60 °*tan20° -1)
=tan70°*cos10°*[(sin60 °*sin20°/cos60°*cos20°)-1]
=tan70°*cos10°*(sin60 °*sin20°-cos60°*cos20°)/(cos60 °*cos20°)
=tan70°*cos10°*[-cos(60°+20°)]/(cos60 °*cos20°)
=-tan70°*cos10°*cos80°/(cos60 °*cos20°)
=-tan70°*cos10°*sin10°/(cos60 °*cos20°)
=-(sin70°/cos70°)*(1/2)*sin20°/(cos60 °*cos20°)
=-(cos20°/sin20°)*sin20°/(2cos60 °*cos20°)=-1/(2cos60 °)=-1/4
(4)=sin50(1+√3tan10)=sin50(cos10+√3sin10)/cos10=sin50*2sin(10+30)/cos10=2sin50sin40/cos10=2sin50cos50/cos10=sin100/cos10=sin80/cos10=cos10/cos10=1