Using standard series from the List of Formulae (MF26), find the Maclaurin expansion of \(\frac{1}{{

Question

Using standard series from the List of Formulae (MF26), find the Maclaurin expansion of $\frac{1}{{{\left( 1+\cos x \right)}^{2}}}$ in ascending powers of $x$ up to and including the term in ${{x}^{4}}$.[4] Find the set of values of $x$ for which $\frac{1}{{{\left( 1+\cos x \right)}^{2}}}$ is within $\pm \,0.5$ of the polynomial found in part (a), where $0\le x < \pi $.[3]

Accepted Answer

(a) $\displaystyle\frac1{(1+\cos x)^2}=\frac14+\frac{x^2}{8}+\frac{7x^4}{192}+O(x^6)$ (b) $0\le x\le1.75$ (3 s.f.)

2024 HCI P2 Q5

2024 HCI P2 Q5

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