Edexcel AEA 2014 June — Question 2 6 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2014
SessionJune
Marks6
PaperDownload PDF ↗
TopicQuadratic trigonometric equations
TypeDirect solve: tanθ equation factorisation
DifficultyChallenging +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.
Spec1.05j 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]

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]}}