Question 7 - A-Level Maths

Show that \(2 \operatorname { cosec } 2 \theta \cot \theta \equiv \operatorname { cosec } ^ { 2 } \theta\).
Hence show that \(\operatorname { cosec } ^ { 2 } 15 ^ { \circ } \tan 15 ^ { \circ } = 4\).
Solve the equation \(2 \operatorname { cosec } \phi \cot \frac { 1 } { 2 } \phi + \operatorname { cosec } \frac { 1 } { 2 } \phi = 12\) for \(- 360 ^ { \circ } < \phi < 360 ^ { \circ }\). Show all necessary working.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.