2025 IGCSE Additional Mathematics October/November 0606/13 Q6

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 \(\sec30^\circ\).[3]

Show that \(\dfrac1{\sec x-1}+\dfrac1{\sec x+1}\) can be written as \(2\operatorname{cosec}x\cot x\).[4]