In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Show that
$$\frac{1 - \cos 2\theta}{\sin^2 2\theta} = k \sec^2 \theta \quad \theta = \frac{n\pi}{2} \quad n \in \mathbb{Z}$$
where \(k\) is a constant to be found.
[3]
- Hence solve, for \(-\frac{\pi}{2} < x < \frac{\pi}{2}\)
$$\frac{1 - \cos 2x}{\sin^2 2x} = (1 + 2\tan x)^2$$
Give your answers to 3 significant figures where appropriate.
[4]