Question 5 - A-Level Maths

Prove the identity \(\frac { 1 } { \cos \theta } - \frac { \cos \theta } { 1 + \sin \theta } \equiv \tan \theta\).
Solve the equation \(\frac { 1 } { \cos \theta } - \frac { \cos \theta } { 1 + \sin \theta } + 2 = 0\) for \(0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }\).