OCR H240/02 2018 December — Question 4 10 marks

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2018
SessionDecember
Marks10
TopicStandard trigonometric equations
TypeProve identity then solve
DifficultyStandard +0.3 This is a straightforward trigonometric identity and equation question. Part (a) requires routine manipulation using basic trig identities (tan A = sin A/cos A, sec A = 1/cos A). Part (b) uses the double angle formula for tan 2θ and factorization, which are standard techniques. While it requires multiple steps and careful algebra, it involves no novel insight—just systematic application of A-level trigonometry methods. Slightly easier than average due to being purely procedural.
Spec1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals

In this question you must show detailed reasoning.
  1. Show that \(\cos A + \sin A \tan A = \sec A\). [3]
  2. Solve the equation \(\tan 2\theta = 3 \tan \theta\) for \(0° \leqslant \theta \leqslant 180°\). [7]

In this question you must show detailed reasoning.

\begin{enumerate}[label=(\alph*)]
\item Show that $\cos A + \sin A \tan A = \sec A$. [3]
\item Solve the equation $\tan 2\theta = 3 \tan \theta$ for $0° \leqslant \theta \leqslant 180°$. [7]
\end{enumerate}

\hfill \mbox{\textit{OCR H240/02 2018 Q4 [10]}}