Can you solve this : Tan ½ X = (1 – Cos X) / ( Sin X ) using half angle identities?

Answer 1

let 1/2 x = t

RHS = (1 - cos 2t)/ sin 2t = (1-(1- 2sin ^2t))/sin 2t

= 2 sin ^2 t/ 2 sin t cos t = sin t/cos t = tan t = tan 1/2 x = LHS

Answer 2

Use the fact that sin X/2 = ±√[(1-cosX/2] and cos X/2 = ±√[(1+cosX)/2]. tan X/2 = (sin X/2)/(cos X/2)

Answer 3

Let X / 2 = A
RHS
= (1 - cos 2A) / sin 2A
= [ 1 - (1 - 2 sin ² A) ] / 2 sin A.cos A
= 2 sin ² A / 2 sin A.cos A
= sin A / cos A
= tan A
= tan.(X / 2) = LHS

Answer 4

Let t = tanx/2
Then cosx = 2t/(t^2 +1) and sinx = (t^2 -1)/(t^2 + 1)


etc you'll obtain an equation in the variable t and solve it for t.