Edexcel AEA 2022 June — Question 3 12 marks

Exam BoardEdexcel
ModuleAEA (Advanced Extension Award)
Year2022
SessionJune
Marks12
PaperDownload PDF ↗
TopicReciprocal Trig & Identities
TypeCompound angle with reciprocal functions
DifficultyChallenging +1.8 Part (a) is a straightforward proof using compound angle formulae, accessible to strong A-level students. Part (b) requires recognizing the Pythagorean identity to simplify sec²θ, then applying the compound angle formula for tan(A-B) in reverse, followed by solving a cotangent equation—this multi-step problem-solving with reciprocal functions and non-standard angles elevates it significantly above typical A-level questions but remains within reach of well-prepared students.
Spec1.05h Reciprocal trig functions: sec, cosec, cot definitions and graphs1.05j Trigonometric identities: tan=sin/cos and sin^2+cos^2=11.05l Double angle formulae: and compound angle formulae1.05o Trigonometric equations: solve in given intervals
3.(a)Use the formulae for \(\sin ( A \pm B )\) and \(\cos ( A \pm B )\) to prove that \(\tan \left( 90 ^ { \circ } - \theta \right) \equiv \cot \theta\) (b)Solve for \(0 < \theta < 360 ^ { \circ }\) $$2 - \sec ^ { 2 } \left( \theta + 11 ^ { \circ } \right) = 2 \tan \left( \theta + 11 ^ { \circ } \right) \tan \left( \theta - 34 ^ { \circ } \right)$$ Give each answer as an integer in degrees. 
3.(a)Use the formulae for $\sin ( A \pm B )$ and $\cos ( A \pm B )$ to prove that $\tan \left( 90 ^ { \circ } - \theta \right) \equiv \cot \theta$\\
(b)Solve for $0 < \theta < 360 ^ { \circ }$

$$2 - \sec ^ { 2 } \left( \theta + 11 ^ { \circ } \right) = 2 \tan \left( \theta + 11 ^ { \circ } \right) \tan \left( \theta - 34 ^ { \circ } \right)$$

Give each answer as an integer in degrees.

\hfill \mbox{\textit{Edexcel AEA 2022 Q3 [12]}}
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