Let

1. A student believes that

   $$y=\ln (\cot x)$$

   Explain why the student thinks this. Prove, by counterexample, that the student is not correct.

2. Show that the gradient of the curve at the point where $x=\frac{\pi }{4}$ can be written in simplest form as

   $$\frac{a}{\ln (b)}$$

   where $a,b\in \mathbb{N}$ are integers to be determined.

Give the value of