Prove that 1-cosx/1+cosx=tan^2x/2

Answer 1

(1-cosx)/(1+cosx) * (1-cosx)/(1-cosx)
= (1-cosx)^2 / (1 - cos^2x)
= (1-cosx)^2/sin^2x
= ((1-cosx)/sinx)^2
= tan^2 x/2
from your half-angle formulas