| Exam Board | OCR |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Addition & Double Angle Formulae |
| Type | Show equation reduces to tan form |
| Difficulty | Standard +0.8 This question requires multiple sophisticated steps: expanding sec(x + π/6) using addition formulae, algebraic manipulation to reach the target form, then solving a trigonometric equation that requires factoring or converting to tan form. While the techniques are C3 standard, the multi-step manipulation and non-obvious path from the given to target form makes this moderately harder than average. |
| Spec | 1.05j 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 |
\begin{enumerate}
\item (i) Show that the equation
\end{enumerate}
$$2 \sin x + \sec \left( x + \frac { \pi } { 6 } \right) = 0$$
can be written as
$$\sqrt { 3 } \sin x \cos x + \cos ^ { 2 } x = 0$$
(ii) Hence, or otherwise, find in terms of $\pi$ the solutions of the equation
$$2 \sin x + \sec \left( x + \frac { \pi } { 6 } \right) = 0$$
for $x$ in the interval $0 \leq x \leq \pi$.\\
\hfill \mbox{\textit{OCR C3 Q5 [9]}}