- (a) Use the substitution \(t = \tan \left( \frac { x } { 2 } \right)\) to show that the equation
$$5 \sin x + 12 \cos x = 2$$
can be written in the form
$$7 t ^ { 2 } - 5 t - 5 = 0$$
(b) Hence solve, for \(- 180 ^ { \circ } < x < 180 ^ { \circ }\), the equation
$$5 \sin x + 12 \cos x = 2$$
giving your answers to one decimal place.