Given that $\alpha$ is an acute angle and $\cos\alpha=\frac{1+\sqrt{5}}{4}$, then $\sin\frac{\alpha}{2}=$ A. $\frac{3-\sqrt{5}}{8}$ B. $\frac{-1+\sqrt{5}}{8}$ C. $\frac{3-\sqrt{5}}{4}$ D. $\frac{-1+\sqrt{5}}{4}$
D By the half-angle formula $\sin^2\frac{\alpha}{2}=\frac{1-\cos\alpha}{2}$, we get $\sin\frac{\alpha}{2}=\frac{\sqrt{5}-1}{4}$. Choose D.
Given that $\alpha$ is an acute angle and $\cos\alpha=\frac{1+\sqrt{5}}{4}$, then $\sin\frac{\alpha}{2}=$\\
A. $\frac{3-\sqrt{5}}{8}$\\
B. $\frac{-1+\sqrt{5}}{8}$\\
C. $\frac{3-\sqrt{5}}{4}$\\
D. $\frac{-1+\sqrt{5}}{4}$