- (i) Use the identity for \(\cos ( A + B )\) to prove that
$$\cos 2 x \equiv 2 \cos ^ { 2 } x - 1$$
(ii) Prove that, for \(\cos x \neq 0\),
$$2 \cos x - \sec x \equiv \sec x \cos 2 x$$
(iii) Hence, or otherwise, find the values of \(x\) in the interval \(0 \leq x \leq 180 ^ { \circ }\) for which
$$2 \cos x - \sec x \equiv 2 \cos 2 x$$