Question

If $\tan 3\theta +\tan \theta =2\tan 2\theta$ then $\theta$ is equal to $\left(nϵz\right)$

• A. $n\pi$
• B. $\frac{n\pi }{4}$
• C. $2n\pi$
• D. None of these

Answer 1

The correct option is A $n\pi$

$\tan 3\theta +\tan \theta =2\tan 2\theta$
$\Rightarrow \tan 3\theta -\tan 2\theta =\tan 2\theta -\tan \theta$
$\Rightarrow \frac{\sin 3\theta \cos 2\theta -\cos 3\theta \sin 2\theta }{\cos 3\theta \cos 2\theta }=\frac{\sin 2\theta \cos \theta -\cos 2\theta \sin \theta }{\cos \theta \cos 2\theta }$
$\Rightarrow \frac{\sin \theta }{\cos 3\theta }=\frac{\sin \theta }{\cos 2\theta }$
$\Rightarrow \sin \theta =0$
$\theta =n\pi$
Ans: A