Answer
$sin(22.5^{\circ}) = \sqrt{{\frac{2-\sqrt{2}}{4}}}$
Work Step by Step
$sin~\frac{\theta}{2} = \sqrt{\frac{1-cos~\theta}{2}}$
$sin(22.5^{\circ}) = sin~\frac{45^{\circ}}{2}$
$sin(22.5^{\circ}) = \sqrt{\frac{1-cos~45^{\circ}}{2}}$
$sin(22.5^{\circ}) = \sqrt{\frac{1-\frac{\sqrt{2}}{2}}{2}}$
$sin(22.5^{\circ}) = \sqrt{\frac{\frac{2-\sqrt{2}}{2}}{2}}$
$sin(22.5^{\circ}) = \sqrt{{\frac{2-\sqrt{2}}{4}}}$
