Edexcel AEA 2008 June — Question 3 12 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2008
SessionJune
Marks12
PaperDownload PDF ↗
TopicAddition & Double Angle Formulae
DifficultyChallenging +1.8 Part (a) requires proving a specific trigonometric value using compound angle formulas or half-angle identities, which is non-routine. Part (b) involves expanding a product of sines, applying product-to-sum formulas or compound angles, then solving a trigonometric equation with surds—requiring multiple sophisticated steps and algebraic manipulation beyond standard A-level. The combination of proof and complex equation-solving with the specific constant from part (a) makes this substantially harder than typical questions.
Spec1.05g Exact trigonometric values: for standard angles1.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

  1. Prove that \(\tan 15° = 2 - \sqrt{3}\) [4]
  2. Solve, for \(0 < \theta < 360°\), $$\sin(\theta + 60°) \sin(\theta - 60°) = (1 - \sqrt{3}) \cos^2 \theta$$ [8]

\begin{enumerate}[label=(\alph*)]
\item Prove that $\tan 15° = 2 - \sqrt{3}$ [4]
\item Solve, for $0 < \theta < 360°$,
$$\sin(\theta + 60°) \sin(\theta - 60°) = (1 - \sqrt{3}) \cos^2 \theta$$ [8]
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2008 Q3 [12]}}