When tanx=1, what does x equal?

May 23, 2016

$x = n \pi + \frac{\pi}{4}$, where $n$ is an integer.

Explanation:

$\tan x = 1$, but as $\tan \left(\frac{\pi}{4}\right) = 1$

However, as period of tan function is $\pi$ and the function repeats after every $\pi$,

the general solution for $\tan x = 1 = \tan \left(\frac{\pi}{4}\right)$ is

$x = n \pi + \frac{\pi}{4}$, where $n$ is an integer.