Show that the equation
$$\sin \left( x - 60 ^ { \circ } \right) - \cos \left( 30 ^ { \circ } - x \right) = 1$$
can be written in the form \(\cos x = k\), where \(k\) is a constant.
Hence solve the equation, for \(0 ^ { \circ } < x < 180 ^ { \circ }\).