sqrt(3)=tan60
1+sqrt(3)*tan10=1+tan60tan10=(sin60sin10+cos60cos10)/cos60cos10=cos50/cos60cos10=2cos50/cos10
sqrt(2sin80*sin80)=sqrt(2)sin80=sqrt(2)cos10
[2sin50+sin10(1+sqrt3*tan10)]*sqrt(2sin80*sin80)=[2sin50+2cos50sin10/cos10]sqrt(2)cos10=2sqrt(2)*(sin50cos10+cos50sin10)=2sqrt(2)*sin60=sqrt(6)