반각 탄젠트와 사인 합

$\displaystyle \tan \frac{\theta}{2} = \frac{1}{2}$ $\displaystyle ( 0 < \theta < \frac{\pi}{2} )$이므로 $\displaystyle \sin \frac{\theta}{2} = \frac{\sqrt{5}}{5}$, $\displaystyle \cos \frac{\theta}{2} = \frac{2 \sqrt{5}}{5}$이다. $\displaystyle \sin \frac{\theta}{2} + \sin \frac{3 \theta}{2}$$\displaystyle = 2 \sin \theta \cos \frac{\theta}{2}$$\displaystyle = 4 \sin \frac{\theta}{2} \cos ^{2} \frac{\theta}{2}$ $\displaystyle = 4 \times \frac{\sqrt{5}}{5} \times \frac{4}{5} = \frac{16 \sqrt{5}}{25}$