The principal solution of the equation $\tan x=1$ is

The correct option is C $\frac{\pi }{4},\frac{3\pi }{4}$
Given: $\tan x=1$
We want to find the principal solution for the given equation.
Now, $\tan x>0$ for $x$ in 1st and 3rd quadrant given as:
$x=\theta \&x=\pi +\theta$
We can find $\theta$ as the solution of the equation:
$\tan x=1\Rightarrow x=\frac{\pi }{4}$
In 3rd quadrant, the angle is given as $\pi +\theta$
$\tan x=1\Rightarrow x=\pi +\frac{\pi }{4}=\frac{5\pi }{4}$
Thus, the principal solution is given as:
$x=\frac{\pi }{4}\&x=\frac{5\pi }{4}$