Question 4 - A-Level Maths

Show that \(\sec ^ { 4 } \theta - \tan ^ { 4 } \theta \equiv 1 + 2 \tan ^ { 2 } \theta\).
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Hence or otherwise solve the equation \(\sec ^ { 4 } 2 \alpha - \tan ^ { 4 } 2 \alpha = 2 \tan ^ { 2 } 2 \alpha \sec ^ { 2 } 2 \alpha\) for \(0 ^ { \circ } < \alpha < 180 ^ { \circ }\). [5]