(a)[2]
Show that the equation $\dfrac{\tan x + \sin x}{\tan x - \sin x} = k$, where $k$ is a constant, can be rewritten in the form $\dfrac{1 + \cos x}{1 - \cos x} = k$.
(b)[2]
Hence express $\cos x$ in terms of $k$.
(c)[2]
Hence solve the equation $\dfrac{\tan x + \sin x}{\tan x - \sin x} = 4$ when $-\pi < x < \pi$.