9 \end{array} \right)$$ where \(\mu\) is a scalar parameter.
(b) Show that \(l _ { 1 }\) and \(l _ { 2 }\) do not meet. The point \(C\) is on \(l _ { 2 }\) where \(\mu = - 1\)
(c) Find the acute angle between \(A C\) and \(l _ { 2 }\) Give your answer in degrees to one decimal place.

1. (a) Find the derivative with respect to \(y\) of

$$\frac { 1 } { ( 1 + 2 \ln y ) ^ { 2 } }$$ (b) Hence find a general solution to the differential equation $$3 \operatorname { cosec } ( 2 x ) \frac { \mathrm { d } y } { \mathrm {~d} x } = y ( 1 + 2 \ln y ) ^ { 3 } \quad y > 0 \quad - \frac { \pi } { 2 } < x < \frac { \pi } { 2 }$$ (c) Show that the particular solution of this differential equation for which \(y = 1\) at \(x = \frac { \pi } { 6 }\) is given by $$y = \mathrm { e } ^ { A \sec x - \frac { 1 } { 2 } }$$ where \(A\) is an irrational number to be found.
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