Question

The value of $\sin \left({22}^{\circ }{30}^{\prime }\right)$ is

• A. $\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$
• B. $\sqrt{\sqrt{2}-1}$
• C. $\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$
• D. None of these

Answer 1

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

We know ${\sin }^{2}A=\left(\frac{1-\cos 2A}{2}\right)$
Therefore, ${\sin }^2\left({22}^{\circ }{30}^{\prime }\right)=\frac{1-\cos {45}^{\circ }}{2}$
$=\frac{(1-\frac{1}{\sqrt{2}})}{2}$
$=\frac{\sqrt{2}-1}{2\sqrt{2}}$
$\Rightarrow \sin \left({22}^{\circ }{30}^{\prime }\right)=\sqrt{\frac{\sqrt{2}-1}{2\sqrt{2}}}$