Question

The most general values of $\theta$ satisfying $\tan \theta +\tan (\frac{3\pi }{4}+\theta )=2$ are

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Here, $\tan \theta +\frac{-1+\tan \theta }{1+\tan \theta }=2$
$\Rightarrow \tan \theta +ta{n}^2\theta -1+\tan \theta =2+2\tan \theta$
$\Rightarrow {\tan }^2\theta =3$
$\Rightarrow \theta =n\pi \pm \frac{\pi }{3}$