(a)

(i) Show that

\(\sin x\tan x+\cos x=\operatorname{sec}x.\)

(ii) Hence solve the equation

\(\sin\frac{\theta}{2}\tan\frac{\theta}{2}+\cos\frac{\theta}{2}=4\)

for \(0\leqslant\theta\leqslant4\pi\), where \(\theta\) is in radians.

(b) Solve the equation

\(\operatorname{cot}(y+38^\circ)=\sqrt3\)

for \(0^\circ\leqslant y\leqslant360^\circ\).