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
$\cos 22\frac{1^{\circ }}{2}=\sqrt{\frac{1+\cos 45^{\circ }}{2}}$
$\left[\because \cos 22\frac{1^{\circ }}{2}is+ve\right]$
$\Rightarrow \cos 22\frac{1^{\circ }}{2}=\sqrt{\frac{1+1/\sqrt{2}}{2}}=\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}$