Question 8 - A-Level Maths

Given that \(y = \sec x\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \sec x \tan x\).
In this question you must show detailed reasoning. Find the exact value of \(\int _ { \frac { 1 } { 12 } \pi } ^ { \frac { 1 } { 6 } \pi } ( \sec 2 x + \tan 2 x ) ^ { 2 } \mathrm {~d} x\).