(a) It is given that

\(2+\cos\theta=x,\qquad 1\lt x\lt 3\)

and

\(2\operatorname{cosec}\theta=y,\qquad y\gt 2.\)

Find \(y\) in terms of \(x\).

(b) Solve the equation

\(3\cos\frac{\phi}{2}=\sqrt3\sin\frac{\phi}{2}\)

for

\(-4\pi\lt \phi\lt 4\pi.\)

Solve the equation

\(3\sin\left(2x+\frac{\pi}{4}\right)=\sqrt3\cos\left(2x+\frac{\pi}{4}\right),\)

for \(0\leq x\leq\pi\).

Solve the equation

\(\sqrt2\cos(3x+1.2)=2\sin(3x+1.2),\)

where \(x\) is in radians, for \(-1.5\leq x\leq1.5\).

Solve the equation

\(\operatorname{cot}\left(2x+\frac{\pi}{3}\right)-\sqrt3=0,\)

where \(-\pi\lt x\lt \pi\) radians. Give your answers in terms of \(\pi\).

Solve the equation

\(\operatorname{cot}^2\left(2x-\frac{\pi}{3}\right)=\frac13,\)

where \(x\) is in radians and \(0\leq x\lt \pi\).

Solve \(1+\sqrt2\sin(x+50^\circ)=0\), for \(-180^\circ\leq x\leq180^\circ\).