| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2014 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Quadratic trigonometric equations |
| Type | Direct solve: tanθ equation factorisation |
| Difficulty | Challenging +1.2 This is an AEA question requiring algebraic manipulation of a trigonometric equation to convert it into a form solvable for tan x. While it involves multiple steps (rearranging, using sin²x + cos²x = 1, dividing by cos²x, and solving a quadratic in tan x), the techniques are standard for students who have practiced such problems. The 6-mark allocation and AEA context place it above average difficulty, but it doesn't require particularly novel insight—just systematic application of known identities and algebraic techniques. |
| Spec | 1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05o Trigonometric equations: solve in given intervals |
Given that
$$3\sin^2 x + 2\sin x = 6\cos x + 9\sin x \cos x$$
and that $-90° < x < 90°$,
find the possible values of $\tan x$.
[6]
\hfill \mbox{\textit{Edexcel AEA 2014 Q2 [6]}}