Solve each equation, giving your answers in exact form.
\(\mathrm { e } ^ { 4 x - 3 } = 2\)
\(\quad \ln ( 2 y - 1 ) = 1 + \ln ( 3 - y )\)
(i) Prove, by counter-example, that the statement
"cosec \(\theta - \sin \theta > 0\) for all values of \(\theta\) in the interval \(0 < \theta < \pi\) " is false.
Find the values of \(\theta\) in the interval \(0 < \theta < \pi\) such that
$$\operatorname { cosec } \theta - \sin \theta = 2$$
giving your answers to 2 decimal places.