- In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
- Prove that
$$\cot ^ { 2 } x - \tan ^ { 2 } x \equiv 4 \cot 2 x \operatorname { cosec } 2 x \quad x \neq \frac { n \pi } { 2 } \quad n \in \mathbb { Z }$$
- Hence solve, for \(- \frac { \pi } { 2 } < \theta < \frac { \pi } { 2 }\)
$$4 \cot 2 \theta \operatorname { cosec } 2 \theta = 2 \tan ^ { 2 } \theta$$
giving your answers to 2 decimal places.