Chapter 5.2, Problem 65ES

(a) Show that

$F\left(x\right)={\tan }^{-1}x$ and $G\left(x\right)=-{\tan }^{-1}\left(1/x\right)$

differ by a constant on the interval $\left(0,+\infty \right)$ by showing that they are antiderivatives of the same function.

(b) Find the constant $C$ such that $F\left(x\right)-G\left(x\right)=C$ by evaluating the functions $F\left(x\right)$ and $G\left(x\right)$ at a particular value of $x$ .

(c) Check your answer to part (b) by using trigonometric identities.