Q. Prove that : tan20 + 4sin20 = root 3

Soln:
L.H.S.
= tan20 + 4sin20

= sin20/cos20 + 4sin20

= (sin20 + 4sin20.cos20)/(cos20)

= (sin20 + 2sin40)/cos20

= [sin20 + 2sin(60-20)]/cos20

= (sin20 + 2sin60.cos20 – 2cos60.sin20)/cos20

= (sin20 + 2sin60.cos20 – sin20)/cos20

= [2.(Ö3/2).cos20]/cos20

= Ö3 R.H.S.