Question

If $\tan \theta +\cot \theta =2,$ then $\sin \theta =$

• A. $\pm \frac{1}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\pm \frac{1}{3}$
• D. $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is B $\frac{1}{\sqrt{2}}$

$\tan \theta +\cot \theta =2$

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

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

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

$\Rightarrow {\tan }^2\theta -2\tan \theta +1=0$

$\Rightarrow {(\tan \theta -1)}^2=0$

$\Rightarrow \tan \theta =1$

$\Rightarrow \theta =45°$

$\therefore \sin \theta =\sin 45°=\frac{1}{\sqrt{2}}$

Hence, the answer is $\frac{1}{\sqrt{2}}.$