| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2015 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Standard trigonometric equations |
| Type | Rational trig expressions |
| Difficulty | Challenging +1.8 This AEA question requires multiple sophisticated steps: recognizing the cotangent-tangent relationship, manipulating the secant product term, applying double angle formulas, and solving a resulting trigonometric equation with the specific angle 78°. While systematic, it demands strong algebraic manipulation skills and non-routine insight to connect the terms, placing it well above average difficulty but not at the extreme end of AEA questions. |
| 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 formulae1.05o Trigonometric equations: solve in given intervals |
Solve for $0 < x < 360°$
$$\cot 2x - \tan 78° = \frac{(\sec x)(\sec 78°)}{2}$$
where $x$ is not an integer multiple of $90°$
[9]
\hfill \mbox{\textit{Edexcel AEA 2015 Q3 [9]}}