(a)[4]
Show that the equation $\frac{\tan x + \cos x}{\tan x - \cos x} = k$, with $k$ a constant, may be rewritten as $(k + 1)\sin^2 x + (k - 1)\sin x - (k + 1) = 0$.
(b)[4]
Hence solve the equation $\dfrac{\tan x + \cos x}{\tan x - \cos x} = 4$ for $0^\circ \leq x \leq 360^\circ$.