Question

Find principal solution for $\tan x=-1$. $xϵ(\frac{\pi }{2},\pi )$

Answer 1

$\tan x=-1$

Here, tan is negative.

We know, tan is negative in 2nd and 4th quadrant.

Here, $\theta ={45}^o$

Value in 2nd quadrant = ${180}^o-{45}^o={135}^o$

Value in 4th quadrant = ${360}^o-{45}^o={315}^o$

So, principal solutions are

$x={135}^o=\frac{3\pi }{4}$ and $x={315}^o=\frac{7\pi }{4}$.