Given that tan x /2 = 1 − cos x /sin x , clearly deduce that tan x/ 12 = 2 − √ 3. [4]

Question

Given that tan x /2 = 1 − cos x/ sin x , clearly deduce that tan x/ 12 = 2 − √ 3. [4]

Answer 1

tan(x/2) = (1 - cosx) / sinx

So, tan(π/12) = tan [(π/6) / 2] = (1 - cos(π/6)) / sin(π/6) = (1 - √3/2) / (1/2) = 2(1 - √3/2) = 2 - √3