(a) Show that

\(\displaystyle \frac{\sin x}{\tan x-1}-\frac{\cos x}{\tan x+1} =\frac{\cos x}{\sin^2x-\cos^2x}.\)

(b) Hence solve the equation

\(\displaystyle \frac{\sin x}{\tan x-1}-\frac{\cos x}{\tan x+1}=1\)

for \(0^\circ\lt x\lt360^\circ\).