- (a) Show that
$$\frac { \cot ^ { 2 } x } { 1 + \cot ^ { 2 } x } \equiv \cos ^ { 2 } x$$
(b) Hence solve, for \(0 \leqslant x < 360 ^ { \circ }\),
$$\frac { \cot ^ { 2 } x } { 1 + \cot ^ { 2 } x } = 8 \cos 2 x + 2 \cos x$$
Give each solution in degrees to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)