| Exam Board | Edexcel |
|---|---|
| Module | C3 (Core Mathematics 3) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Harmonic Form |
| Type | Solve reciprocal trig equation |
| Difficulty | Standard +0.3 This is a standard C3 harmonic form question with straightforward algebraic manipulation. Part (a) is routine application of the R-formula, part (b) requires multiplying through by sin x cos x (a common technique), and part (c) is simply substituting results. While multi-step, each component follows well-practiced procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^21.05l Double angle formulae: and compound angle formulae1.05n Harmonic form: a sin(x)+b cos(x) = R sin(x+alpha) etc |
\begin{enumerate}[label=(\alph*)]
\item Express $\sin x + \sqrt{3} \cos x$ in the form $R \sin (x + \alpha)$, where $R > 0$ and $0 < \alpha < 90°$. [4]
\item Show that the equation $\sec x + \sqrt{3} \cosec x = 4$ can be written in the form
$$\sin x + \sqrt{3} \cos x = 2 \sin 2x.$$ [3]
\item Deduce from parts (a) and (b) that $\sec x + \sqrt{3} \cosec x = 4$ can be written in the form
$$\sin 2x - \sin (x + 60°) = 0.$$ [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C3 Q23 [8]}}