(1-cosx)/sinx=sinx(1-cosx)/sin²x =sinx(1-cosx)/(1-cos²x) =sinx(1-cosx)/(1+cosx)(1-cosx)=sinx/(1+cosx)=2sin(x/2)cos(x/2)/2cos²(x/2) =sin(x/2)/cos(x/2)=tan(x/2)