Question

Show that
2 tan 20 + 4 tan 40 + 8 tan 80 = 9(cot 10-tan 10)

Answer 1

We need to proceed as follows :

First we prove that tan x = (cotx - cot2x)

cot x - tan x = cos x/ sin x - sin x/ cos x
= (cos^2 x - sin ^2 x) /( sinx * cos x)
= cot 2x

cotx - tanx = cot2x
so tan x = cot x - cot 2x