- (a) Prove that
$$\frac { 1 - \cos 2 x } { 1 + \cos 2 x } \equiv \tan ^ { 2 } x , \quad x \neq ( 2 n + 1 ) 90 ^ { \circ } , n \in \mathbb { Z }$$
(b) Hence, or otherwise, solve, for \(- 90 ^ { \circ } < \theta < 90 ^ { \circ }\),
$$\frac { 2 - 2 \cos 2 \theta } { 1 + \cos 2 \theta } - 2 = 7 \sec \theta$$
Give your answers in degrees to one decimal place.
(Solutions based entirely on graphical or numerical methods are not acceptable.)