- (a) Using the identity for \(\cos ( A + B )\), prove that
$$\cos 2 A \equiv 2 \cos ^ { 2 } A - 1$$
(b) Hence, using algebraic integration, find the exact value of
$$\int _ { \frac { \pi } { 12 } } ^ { \frac { \pi } { 8 } } \left( 5 - 4 \cos ^ { 2 } 3 x \right) d x$$