Question

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

then the value of ${\tan }^{{}^2}\theta +\frac{1}{{\tan }^2\theta }$ will be :

• A. $4$
• B. $2$
• C. $1$
• D. $8$

Answer 1

Answer: (B)

$2$

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

Squaring both sides, we get

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

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

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

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

Hence, the answer is $2.$