Question

The value of $\cos 22 \frac{1^{\circ}}{2}$ is

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

Answer 1

Answer: (C)

We have,
$\cos \frac{A}{2} = \pm \sqrt{ \frac{1 + \cos A}{2}}$
Putting $A = 45^{\circ}$ , we get
$\cos 22 \frac{1^{\circ}}{2} = \sqrt{\frac{1 + \cos 45^{\circ}}{2}}$
$\left[ \because \cos22 \frac{1^{\circ}}{2} is + ve \right] $
$\Rightarrow \cos22 \frac{1^{\circ}}{2} = \sqrt{\frac{1+1/\sqrt{2}}{2}} = \sqrt{\frac{\sqrt{2} + 1}{2\sqrt{2}} }$