Question

$\text{The principal solution of}\tan \theta =-1\text{is}$

Answer 1

Given,
$\tan \theta =-1$
Principal solution when $0\le x\le 2\pi$
$\tan \theta$ lies in either 2nd or 4th quadrant.
If $\tan \theta =-1\Rightarrow \tan \theta =-\tan \frac{\pi }{4}\Rightarrow \tan \theta =\tan (\frac{-\pi }{4})\Rightarrow \theta =n\pi -\frac{\pi }{4}\text{where}n\in Z$
$\text{put}n=0$
$\Rightarrow \theta =-\frac{\pi }{4}$
Hence the correct answer is Option a.