# 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 $$a$$.

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