Question

If $tan\alpha +cot\alpha =2$ then $\sqrt{tan\alpha }+\sqrt{cot\alpha }=$

• A. $\pm \sqrt{2}$
• B. $\pm 2\sqrt{2}$
• C. $\pm 2$
• D. $\pm 4\sqrt{2}$

Answer 1

The correct option is C $\pm 2$

We can write

$(\sqrt{\tan \alpha }+\sqrt{\cot \alpha }{)}^2=\tan \alpha +\cot \alpha +2\sqrt{\tan \alpha }\sqrt{\cot \alpha }\Rightarrow (\sqrt{\tan \alpha }+\sqrt{\cot \alpha }{)}^2=2+2.\sqrt{\tan \alpha }.\frac{1}{\sqrt{\tan \alpha }}=2+2=4\Rightarrow (\sqrt{\tan \alpha }+\sqrt{\cot \alpha }{)}^2=4\Rightarrow \sqrt{\tan \alpha }+\sqrt{\cot \alpha }=\pm 2$

So, the Correct Answer will either be 2 or -2