Question

If $\tan$ $\theta +\frac{1}{\tan \theta }=2$, then find the value of ${\tan }^2\theta +\frac{1}{{\tan }^2\theta }$ is :

• A. $3$
• B. $4$
• C. $2$
• D. $-4$

Answer 1

Answer: (C)

$2$

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

Squaring both sides, we get

$\Rightarrow {(\tan \theta +\frac{1}{\tan \theta })}^2=4$

$\Rightarrow {\tan }^2\theta +\frac{1}{{\tan }^2\theta }+2=4$

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

Hence, the answer is $2.$