Question

If $\tan \theta +\cot \theta =2$, then the value of ${\tan }^2\theta +{\cot }^2\theta$ is ____________.

• A. $4$
• B. $2$
• C. $\frac{3}{2}$
• D. $5$

Answer 1

Answer: (B)

$2$

We know $tan\theta =\frac{1}{cot\theta }$,

So, $(tan\theta +cot\theta {)}^2=ta{n}^2\theta +co{t}^2\theta +2$

$\Rightarrow (2{)}^2=ta{n}^2\theta +co{t}^2\theta +2$

$\Rightarrow ta{n}^2\theta +co{t}^2\theta =2^2-2$

$\Rightarrow ta{n}^2\theta +co{t}^2\theta =2$

So, Option (B)