Tan20+4sin20=√3

Answer 1

Reiny already showed you that this can not be true.
http://www.jiskha.com/display.cgi?id=1442757482

Answer 2

Ahhh, you changed it

LS = sin20/cos20 + 4sin20
= sin20/cos20 + 4sin20cos20/cos20
= (sin20 + 4sin20cos20)/cos20
= (sin 20 + 2sin40)/cos20
= (sin20 + 2sin(60-20))/cos20
= (sin20 + 2sin60cos20 - 2cos60sin20)/cos20
= (sin20 + √3 cos20 - sin20)/cos20
= √3cos20/cos20
= √3