Question 8 - A-Level Maths

Given that $\cos \theta \neq \pm 1$, prove the identity $$\frac { 1 } { 1 - \cos \theta } + \frac { 1 } { 1 + \cos \theta } \equiv 2 \operatorname { cosec } ^ { 2 } \theta$$ 8
Hence, find the set of values of $A$ for which the equation $$\frac { 1 } { 1 - \cos \theta } + \frac { 1 } { 1 + \cos \theta } = A$$ has real solutions.
Fully justify your answer.
8
Given that $\theta$ is obtuse and $$\frac { 1 } { 1 - \cos \theta } + \frac { 1 } { 1 + \cos \theta } = 16$$ find the exact value of $\cot \theta$