Solve the equation \(\sec x = - 5\), giving all values of \(x\) in radians to two decimal places in the interval \(0 < x < 2 \pi\).
Show that the equation
$$\frac { \operatorname { cosec } x } { 1 + \operatorname { cosec } x } - \frac { \operatorname { cosec } x } { 1 - \operatorname { cosec } x } = 50$$
can be written in the form
$$\sec ^ { 2 } x = 25$$
Hence, or otherwise, solve the equation
$$\frac { \operatorname { cosec } x } { 1 + \operatorname { cosec } x } - \frac { \operatorname { cosec } x } { 1 - \operatorname { cosec } x } = 50$$
giving all values of \(x\) in radians to two decimal places in the interval \(0 < x < 2 \pi\).
(3 marks)