Question 7 - A-Level Maths

Prove that \(2 \sin \theta \operatorname { cosec } 2 \theta \equiv \sec \theta\).
Solve the equation \(\tan ^ { 2 } \theta + 7 \sin \theta \operatorname { cosec } 2 \theta = 8\) for \(- \pi < \theta < \pi\).
Find \(\int 8 \sin ^ { 2 } \frac { 1 } { 2 } x \operatorname { cosec } ^ { 2 } x d x\).
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