Standard +0.3 This is a straightforward algebraic manipulation using standard identities (tan θ = sin θ/cos θ, sin²θ + cos²θ = 1) to convert to quadratic form, followed by routine solving and application of double angle. The steps are mechanical and well-practiced, making it slightly easier than average.
9. (a) Show that the equation
$$\cos \theta - 1 = 4 \sin \theta \tan \theta$$
can be written in the form
$$5 \cos ^ { 2 } \theta - \cos \theta - 4 = 0$$
(b) Hence solve, for \(0 \leqslant x < \frac { \pi } { 2 }\)
$$\cos 2 x - 1 = 4 \sin 2 x \tan 2 x$$
giving your answers, where appropriate, to 2 decimal places.
9. (a) Show that the equation
$$\cos \theta - 1 = 4 \sin \theta \tan \theta$$
can be written in the form
$$5 \cos ^ { 2 } \theta - \cos \theta - 4 = 0$$
(b) Hence solve, for $0 \leqslant x < \frac { \pi } { 2 }$
$$\cos 2 x - 1 = 4 \sin 2 x \tan 2 x$$
giving your answers, where appropriate, to 2 decimal places.\\
\hfill \mbox{\textit{Edexcel P2 2019 Q9 [8]}}