Given $0 < a < \pi$, $\cos \frac{a}{2} = \frac{\sqrt{5}}{5}$, then $\sin\left(a - \frac{\pi}{4}\right) = $ A. $\frac{\sqrt{2}}{10}$ B. $\frac{\sqrt{2}}{5}$ C. $\frac{3\sqrt{2}}{10}$ D. $\frac{7\sqrt{2}}{10}$
Given $0 < a < \pi$, $\cos \frac{a}{2} = \frac{\sqrt{5}}{5}$, then $\sin\left(a - \frac{\pi}{4}\right) = $\\
A. $\frac{\sqrt{2}}{10}$\\
B. $\frac{\sqrt{2}}{5}$\\
C. $\frac{3\sqrt{2}}{10}$\\
D. $\frac{7\sqrt{2}}{10}$