- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Determine, in ascending powers of \(\left( x - \frac { \pi } { 6 } \right)\) up to and including the term in \(\left( x - \frac { \pi } { 6 } \right) ^ { 3 }\), the Taylor series expansion about \(\frac { \pi } { 6 }\) of
$$y = \tan \left( \frac { 3 x } { 2 } \right)$$
giving each coefficient in simplest form.
- Hence show that
$$\tan \frac { 3 \pi } { 8 } \approx 1 + \frac { \pi } { 4 } + \frac { \pi ^ { 2 } } { A } + \frac { \pi ^ { 3 } } { B }$$
where \(A\) and \(B\) are integers to be determined.