Show that 1-cos theta/1+cos theta = tan1/2 theta

Answer 1

(1-cosx)/(1+cosx)

= tan ? it's unclear what the right side is

a disproof is just one counterexample, try 45 degrees

(1-cos45)/(1+cos45)

= .293/1.707

= about .172

the right side is tangent of 45 degrees = 1 which doesn't = .172

but tan^2(45/2) = tan^2(22.5) = .172

the problem then seems to be

(1-cosx)/(1+cosx) = tan^2(x/2)

the half angle formula for tangent

is

tan(x/2) = sqr[(1-cosx)/(1+cosx)]

square both sides:

tan^2(x/2) = (1-cosx)/(1+cosx)