4 It is given that \(\tan ^ { 2 } x = \sec x + 11\).
- Show that the equation \(\tan ^ { 2 } x = \sec x + 11\) can be written in the form
$$\sec ^ { 2 } x - \sec x - 12 = 0$$
- Hence show that \(\cos x = \frac { 1 } { 4 }\) or \(\cos x = - \frac { 1 } { 3 }\).
- Hence, or otherwise, solve the equation \(\tan ^ { 2 } x = \sec x + 11\), giving all values of \(x\) to the nearest degree in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\).