Simplify single fraction to numerical value

A question is this type if and only if it asks to find an approximate numerical value of a single fraction containing trigonometric functions of small angle θ, without requiring further algebraic manipulation.

3 questions · Standard +0.3

1.05e Small angle approximations: sin x ~ x, cos x ~ 1-x^2/2, tan x ~ x
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Edexcel PMT Mocks Q1
3 marks Standard +0.8
  1. Given that \(\theta\) is small and is measured in radians, use the small angle approximations to find an approximate value of
$$\frac { \theta \tan 3 \theta } { \cos 2 \theta - 1 }$$
Edexcel Paper 1 2018 June Q1
3 marks Moderate -0.3
  1. Given that \(\theta\) is small and is measured in radians, use the small angle approximations to find an approximate value of
$$\frac { 1 - \cos 4 \theta } { 2 \theta \sin 3 \theta }$$ (3)
Edexcel Paper 2 2024 June Q5
3 marks Standard +0.3
  1. Given that \(\theta\) is small and in radians, use the small angle approximations to find an approximate numerical value of
$$\frac { \theta \tan 2 \theta } { 1 - \cos 3 \theta }$$