Find the exact value of tan 5pi/12 using the half-angle identity.

Answer 1

tan 5pi/6 = -1/√3

tan x/2 = (1-cos(x))/sin(x)

cos 5pi/6 = -√3/2
sin 5pi/6 = 1/2

tan 5pi/12 = (1 + √3/2)/(1/2)
= 2 + √3