Question

If $\tan \theta +\tan (\frac{3\pi }{4}+\theta )=2$ then find the value of ${\tan }^2\theta$

Answer 1

$\tan \theta +\tan (\frac{3\pi }{4}+\theta )=2$

$\Rightarrow \tan \theta +\frac{\tan \theta -1}{\tan \theta +1}=2$ $[\because \tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}]$

$\Rightarrow \tan \theta +{\tan }^2\theta -1+\tan \theta =2+2\tan \theta$

$\Rightarrow {\tan }^2\theta =3$