9. (a) Using the formula for \(\sin ( A + B )\) and the relevant double angle formulae, find an
identity for \(\sin 3 x\), giving your answer in the form $$\sin ( 3 x ) \equiv P \sin x + Q \sin ^ { 3 } x$$ where \(P\) and \(Q\) are constants to be determined.
(b) Hence, showing each step of your working, evaluate $$\int _ { \frac { \pi } { 6 } } ^ { \frac { \pi } { 2 } } \sin 3 x \cos x d x$$ (Solutions based entirely on graphical or numerical methods are not acceptable.)