Question 2 - A-Level Maths

Edexcel AEA 2016 June — Question 2 7 marks

Exam Board	Edexcel
Module	AEA (Advanced Extension Award)
Year	2016
Session	June
Marks	7
Paper	Download PDF ↗
Topic	Addition & Double Angle Formulae
Type	Find exact trigonometric values
Difficulty	Challenging +1.8 This AEA question requires combining multiple inverse trigonometric functions using addition formulae and double angle identities. Students must evaluate each term (some non-standard like arctan(1/√2)), apply compound angle formulae correctly, and simplify to a multiple of π. It demands strong technical facility with inverse trig functions and multi-step algebraic manipulation beyond typical A-level questions, but follows a clear path once the approach is identified.
Spec	1.05i Inverse trig functions: arcsin, arccos, arctan domains and graphs

2.Find the value of $$\arccos \left( \frac { 1 } { \sqrt { 2 } } \right) + \arcsin \left( \frac { 1 } { 3 } \right) + 2 \arctan \left( \frac { 1 } { \sqrt { 2 } } \right)$$ Give your answer as a multiple of $\pi$ . $$\text { (arccos } x \text { is an alternative notion for } \cos ^ { - 1 } x \text { etc.) }$$

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2.Find the value of

$$\arccos \left( \frac { 1 } { \sqrt { 2 } } \right) + \arcsin \left( \frac { 1 } { 3 } \right) + 2 \arctan \left( \frac { 1 } { \sqrt { 2 } } \right)$$

Give your answer as a multiple of $\pi$ .

$$\text { (arccos } x \text { is an alternative notion for } \cos ^ { - 1 } x \text { etc.) }$$

\hfill \mbox{\textit{Edexcel AEA 2016 Q2 [7]}}

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