sin(50)*(1+sqrt(3)*tan(10))
=2*sin(50)/cos(10)*(1/2*cos(10)+sqrt(3)/2*sin(10))
=2*sin(50)/cos(10)*(cos(60)*cos(10)+sin(60)*sin(10))
=2*sin(50)/cos(10)*cos(50)
=2*sin(50)*cos(50)/cos(10)
=sin(100)/cos(10)
=cos(10)/cos(10)
=1