Question

If ${\sin }^2\theta +{\text{cosec}}^2\theta$ $=6$, then $\sin \theta +\text{cosec}\theta$ $=$ _____

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

Answer 1

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

Given, ${\sin }^2\theta +{\text{cosec}}^2\theta =6$
$\Rightarrow {\sin }^2\theta +{\text{cosec}}^2\theta +2\times \sin \theta \times \text{cosec}\theta$ $=6+2\sin \theta \times \text{cosec}\theta$

$\Rightarrow (\sin \theta +\text{cosec}\theta {)}^2=6+2$
$\Rightarrow \sin \theta +\text{cosec}\theta =\sqrt{8}$
$\Rightarrow \sin \theta +\text{cosec}\theta =2\sqrt{2}$
Hence, option 'B' is correct.