Challenging +1.3 This question requires systematic application of angle reduction and double angle formulae with nested surds. While the techniques are standard (cos 405° = cos 45°, then repeated half-angle formula), the algebraic manipulation to express the answer in the specific nested surd form requires careful work and is more demanding than typical A-level questions. It's harder than average but not exceptionally difficult for AEA standard.
1.(a)Write down the exact value of \(\cos 405 ^ { \circ }\)
(b)Hence,using a double angle identity for cosine,or otherwise,determine the exact value of \(\cos 101.25 ^ { \circ }\) ,giving your answer in the form
$$a \sqrt { b + c \sqrt { 2 + \sqrt { 2 } } }$$
where \(a\) ,\(b\) and \(c\) are rational numbers.
1.(a)Write down the exact value of $\cos 405 ^ { \circ }$\\
(b)Hence,using a double angle identity for cosine,or otherwise,determine the exact value of $\cos 101.25 ^ { \circ }$ ,giving your answer in the form
$$a \sqrt { b + c \sqrt { 2 + \sqrt { 2 } } }$$
where $a$ ,$b$ and $c$ are rational numbers.
\hfill \mbox{\textit{Edexcel AEA 2023 Q1 [6]}}