12 A curve \(C\) has equation
$$x ^ { 3 } \sin y + \cos y = A x$$
where \(A\) is a constant.
\(C\) passes through the point \(P \left( \sqrt { 3 } , \frac { \pi } { 6 } \right)\)
12
- Show that \(A = 2\)
12 - Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 2 - 3 x ^ { 2 } \sin y } { x ^ { 3 } \cos y - \sin y }\)
12
- (ii) Hence, find the gradient of the curve at \(P\).
12 - (iii) The tangent to \(C\) at \(P\) intersects the \(x\)-axis at \(Q\).
Find the exact \(x\)-coordinate of \(Q\).