- (a) Show that
$$\cot ^ { 2 } x - \operatorname { cosec } x - 11 = 0$$
may be expressed in the form \(\operatorname { cosec } ^ { 2 } x - \operatorname { cosec } x + k = 0\), where \(k\) is a constant.
(b) Hence solve for \(0 \leqslant x < 360 ^ { \circ }\)
$$\cot ^ { 2 } x - \operatorname { cosec } x - 11 = 0$$
Give each solution in degrees to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)