Generalise

Calculus Level 4

\[\large \color{red}{\xi} =\int _{ 0 }^{ { \pi }/{ 2 } }{ \cfrac { 1 }{ 1+\tan ^{ a }{ x } } } \, dx\\ \large \color{blue}{\psi} =\int _{ 0 }^{ { \pi }/{ 2 } }{ \cfrac { 1 }{ 1+\cot ^{ a }{ x } } } \, dx\]

We are given the two integrals \(\color{red}{\xi}\) and \(\color{blue}{\psi}\), where \(a\) is a positive integer.
Which of the following statements is/are true?

(A): The value of \(\color{red}{\xi}\) depends on the value of \(a\).

(B): The value of \(\color{blue}{\psi}\) does not depend on the value of \(a\).

(C): \(\color{red}{\xi}=\color{blue}{\psi}\) for all values of \(a\).


Inspiration from Matthew Scroggs.
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