(a) By writing \(\cot x\) and \(\tan x\) in terms of \(\cos x\) and \(\sin x\), show that

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

(b) Solve the equation \(9\cot x+3\operatorname{cosec}x=\tan x\), for \(0^\circ\lt x\lt360^\circ\).