(a) The diagram shows an equilateral triangle \(ABC\) with side \(a\). \(M\) is the midpoint of \(AC\) and angle \(AMB=90^\circ\).

Use the diagram to find \(\sec30^\circ\).

(b) Show that \(\dfrac{1}{\sec x-1}+\dfrac{1}{\sec x+1}\) can be written as \(2\operatorname{cosec}x\cot x\).