Question 7 - A-Level Maths

Exam Board	AQA
Module	FP2 (Further Pure Mathematics 2)
Year	2014
Session	June
Marks	7
Topic	Integration using inverse trig and hyperbolic functions

Given that \(y = \tan ^ { - 1 } \left( \frac { 1 + x } { 1 - x } \right)\) and \(x \neq 1\), show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 1 + x ^ { 2 } }\).
[0pt] [4 marks]
Hence, given that \(x < 1\), show that \(\tan ^ { - 1 } \left( \frac { 1 + x } { 1 - x } \right) - \tan ^ { - 1 } x = \frac { \pi } { 4 }\).
[0pt] [3 marks]