OCR MEI C4 2016 June — Question 5

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Year2016
SessionJune
TopicReciprocal Trig & Identities

5 In Fig. 5, triangles \(\mathrm { ABC } , \mathrm { ACD }\) and ADE are all right-angled, and angles \(\mathrm { BAC } , \mathrm { CAD }\) and DAE are all \(\theta\). \(\mathrm { AB } = x\) and \(\mathrm { AE } = 2 x\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8b807b2e-777b-4c9a-b3dd-890d21d33174-2_567_465_1905_799} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure}
  1. Show that \(\sec ^ { 3 } \theta = 2\).
  2. Hence show the ratio of lengths ED to CB is \(2 ^ { \frac { 2 } { 3 } } : 1\).