- (a) Use the identities for \(\cos ( A + B )\) and \(\cos ( A - B )\) to prove that
$$\cos P - \cos Q \equiv - 2 \sin \frac { P + Q } { 2 } \sin \frac { P - Q } { 2 }$$
(b) Hence find all solutions in the interval \(0 \leq x < 180\) to the equation
$$\cos 5 x ^ { \circ } + \sin 3 x ^ { \circ } - \cos x ^ { \circ } = 0$$
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