Question 5 - A-Level Maths

Exam Board	OCR
Module	C4 (Core Mathematics 4)
Year	2013
Session	June
Topic	Standard Integrals and Reverse Chain Rule

Show that \(\frac { 1 } { 1 - \tan x } - \frac { 1 } { 1 + \tan x } \equiv \tan 2 x\).
Hence evaluate \(\int _ { \frac { 1 } { 12 } \pi } ^ { \frac { 1 } { 6 } \pi } \left( \frac { 1 } { 1 - \tan x } - \frac { 1 } { 1 + \tan x } \right) \mathrm { d } x\), giving your answer in the form \(a \ln b\).