Show equivalence then solve inequality

A question is this type if and only if after showing a trig equation can be written in quadratic form, the follow-up task is to solve a trig inequality (not just an equation) using the quadratic form.

1 questions · Standard +0.3

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OCR PURE Q6
7 marks Standard +0.3
  1. Show that the equation \(6 \cos ^ { 2 } \theta = \tan \theta \cos \theta + 4\) can be expressed in the form \(6 \sin ^ { 2 } \theta + \sin \theta - 2 = 0\).
  2. \includegraphics[max width=\textwidth, alt={}, center]{d6430776-0b87-4e5e-8f78-c6228ee163d5-4_446_1150_1119_338} The diagram shows parts of the curves \(y = 6 \cos ^ { 2 } \theta\) and \(y = \tan \theta \cos \theta + 4\), where \(\theta\) is in degrees. Solve the inequality \(6 \cos ^ { 2 } \theta > \tan \theta \cos \theta + 4\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\).