Question

If $\tan \theta +\frac{1}{\tan \theta }=2$, then the value to ${\tan }^2\theta +\frac{1}{{\tan }^2\theta }$ is equal to

• A. $6$
• B. $4$
• C. $2$
• D. $3$

Answer 1

The correct option is C $2$

$\tan \Theta +\frac{1}{\tan \Theta }=2$

or, ${\tan }^2\Theta +1=2\tan \Theta$

or, ${\tan }^2\Theta -2\tan \Theta +1=0$

or, $(\tan \Theta -1{)}^2=0$

$\therefore \tan \Theta =1$

${\tan }^2\Theta +\frac{1}{{\tan }^2\Theta }=1+1=2$