2 Express \(y = 2 \sin 2 x - 3 \cos 2 x\) in the form \(y = R \sin ( 2 x - \alpha )\),
where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\)
In this question you must show all of your algebraic steps clearly.
$$f ( x ) = \frac { 1 } { \sqrt { 1 + 2 x } }$$
- Expand \(f ( x )\) in accending powers of \(x\) up to and including the term in \(x ^ { 3 }\).
- Hence, show that \(\frac { 2 - 5 x } { \sqrt { 1 + 2 x } } \approx 2 - 7 x + A x ^ { 2 } + B x ^ { 3 }\), where \(A\) and \(B\) are constants to be found.
- State the set of values of \(x\) for which the expansion in part (ii) is valid.