(a) Show that the equation \(\frac{\tan x + \sin x}{\tan x - \sin x} = k\), where \(k\) is a constant, may be expressed as \(\frac{1 + \cos x}{1 - \cos x} = k\).

(b) Hence express \(\cos x\) in terms of \(k\).

(c) Hence solve the equation \(\frac{\tan x + \sin x}{\tan x - \sin x} = 4\) for \(-\pi < x < \pi\).