(a) Show that

\(\frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x}=2\operatorname{cosec}x.\)

(b) Solve the following equations.

(i) \(\operatorname{cot}^2y+\operatorname{cosec}y-5=0\), for \(0^\circ\le y\le360^\circ\).

(ii) \(\cos\left(2z+\dfrac{\pi}{4}\right)=-\dfrac{\sqrt3}{2}\), for \(0\le z\le\pi\) radians.