Reciprocal expansion to polynomial form

A question is this type if and only if it requires showing that 1/(expression) can be approximated as a polynomial 1 + aθ + bθ² using small angle approximations.

1 questions · Standard +0.3

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WJEC Unit 3 2024 June Q12
6 marks Standard +0.3
  1. Given that \(\theta\) is small, show that \(2\cos\theta + \sin\theta - 1 \approx 1 + \theta - \theta^2\). [2]
  2. Hence, when \(\theta\) is small, show that $$\frac{1}{2\cos\theta + \sin\theta - 1} \approx 1 + a\theta + b\theta^2,$$ where \(a\), \(b\) are constants to be found. [4]