(tan20°-√3)/sin20°
=tan20°/sin20°-√3/sin20°
=1/cos20°-√3/sin20°
=(sin20°-√3cos20°)/(sin20°cos20°)
=4(1/2sin20°-√3/2cos20°)/(2sin20°cos20°)
=4sin(-40°)/sin40°
=-4
(tan20°-√3)/sin20°
=tan20°/sin20°-√3/sin20°
=1/cos20°-√3/sin20°
=(sin20°-√3cos20°)/(sin20°cos20°)
=4(1/2sin20°-√3/2cos20°)/(2sin20°cos20°)
=4sin(-40°)/sin40°
=-4