1/sin10-√3/sin80 =(sin80-√3*sin10)/(sin80*sin10) =(cos10-√3*sin10)/(cos10*sin10) =4(cos10/2-√3*sin10/2)/(2sin10*cos10) =4*(cos60*cos10-sin60*sin10)/sin20 =4*cos(60+10)/sin20 =4*cos70/sin20 =4