Proving inverse trig identities

A question is this type if and only if it asks to prove an identity involving inverse trigonometric functions using differentiation or other methods.

1 questions · Challenging +1.2

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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]