Question

How do you find the exact values of ${\tan }^{-1}\left(1\right)$ ?

Answer 1

Compute the required value.

Given: ${\tan }^{-1}\left(1\right)$

We know that,

$$\begin{gathered} {\tan }^{-1}\left(1\right)={\tan }^{-1}\left(\tan \left(\frac{\mathrm{\pi }}{4}\right)\right) \\ \Rightarrow {\tan }^{-1}\left(1\right)=\frac{\mathrm{\pi }}{4}(\because {\tan }^{-1}\left(t\mathrm{an}\theta \right)=\theta ) \end{gathered}$$

Hence, the exact value of ${\tan }^{-1}\left(1\right)$ is $\frac{\mathrm{\pi }}{4}$.