Standard +0.8 Part (a) is a routine double angle equation requiring standard substitution and factorization. Part (b) is more sophisticated, requiring knowledge that arccos x + arccos y = π/2 implies x² + y² = 1 (or using complementary angle properties), then solving a quartic that reduces to a quadratic. The combination of inverse trig manipulation and algebraic solving elevates this above standard A-level but remains accessible with systematic approach.
3.(a)Solve,for \(0 \leq x < 2 \pi\) ,
$$\cos x + \cos 2 x = 0$$
(b)Find the exact value of \(x , x \geq 0\) ,for which
$$\arccos x + \arccos 2 x = \frac { \pi } { 2 }$$
[ \(\arccos x\) is an alternative notation for \(\cos ^ { - 1 } x\) .]
3.(a)Solve,for $0 \leq x < 2 \pi$ ,
$$\cos x + \cos 2 x = 0$$
(b)Find the exact value of $x , x \geq 0$ ,for which
$$\arccos x + \arccos 2 x = \frac { \pi } { 2 }$$
[ $\arccos x$ is an alternative notation for $\cos ^ { - 1 } x$ .]
\hfill \mbox{\textit{Edexcel AEA 2007 Q3 [11]}}