2020 A-Level H2 Mathematics

It is given that $\mathrm{f}(x)=\ln \left( 1+\sin 3x \right)$.

1. Show that $\mathrm{f}''(x)=\frac{k}{1+\sin 3x}$, where $k$ is a constant to be found.

   [3]

2. Hence find the first three non-zero terms of the Maclaurin expansion of $\mathrm{f}(x)$.

   [4]