| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2021 |
| Session | March |
| Marks | 5 |
| Topic | Reciprocal Trig & Identities |
| Type | Prove identity then solve equation |
| Difficulty | Standard +0.3 Part (i) is a straightforward identity manipulation using tan²θ = sec²θ - 1 and 1/cosθ = secθ (routine recall). Part (ii) requires solving a quadratic in secθ and considering the range of secθ, which is standard A-level technique. The 5-mark total and multi-step nature elevate it slightly above trivial, but it remains easier than average with no novel insight required. |
| 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^21.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}[label=(\roman*)]
\item Express $2 \tan^2 \theta - \frac{1}{\cos \theta}$ in terms of $\sec \theta$. [1]
\item Hence solve, for $0° < \theta < 360°$, the equation
$$2 \tan^2 \theta - \frac{1}{\cos \theta} = 4.$$ [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM 2021 Q2 [5]}}