Standard +0.3 This question requires knowing the standard Maclaurin series for cos(2x), applying the identity sin²x = (1-cos(2x))/2, and performing straightforward algebraic manipulation to extract coefficients. While it involves multiple steps and the identity may not be immediately obvious to all students, it's a fairly standard Further Maths exercise in series manipulation with no novel problem-solving required—slightly easier than average.
5 Using the Maclaurin series for \(\cos 2 x\), show that, for small values of \(x\), \(\sin ^ { 2 } x \approx a x ^ { 2 } + b x ^ { 4 } + c x ^ { 6 }\),
where the values of \(a , b\) and \(c\) are to be given in exact form.
5 Using the Maclaurin series for $\cos 2 x$, show that, for small values of $x$, $\sin ^ { 2 } x \approx a x ^ { 2 } + b x ^ { 4 } + c x ^ { 6 }$,\\
where the values of $a , b$ and $c$ are to be given in exact form.
\hfill \mbox{\textit{OCR MEI Further Pure Core 2019 Q5 [5]}}