| Exam Board | SPS |
|---|---|
| Module | SPS FM (SPS FM) |
| Year | 2021 |
| Session | April |
| Marks | 4 |
| Topic | Standard trigonometric equations |
| Type | Convert to quadratic in tan |
| Difficulty | Challenging +1.2 This question requires converting to a single trigonometric function using the identity tan²θ = sec²θ - 1, then solving a quadratic in sec θ, and finally finding all solutions in the given range. While it involves multiple steps and careful handling of the quadratic (including checking validity of solutions), it's a fairly standard Further Maths trigonometric equation that follows a well-practiced technique, making it moderately above average difficulty. |
| 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 |
solve, for $0° < \theta < 360°$, the equation
$$2 \tan^2 \theta - \frac{1}{\cos \theta} = 4.$$ [4]
\hfill \mbox{\textit{SPS SPS FM 2021 Q2 [4]}}