Answer
$$\sin^2\frac{\pi}{12}=\frac{2-\sqrt3}{4}$$
Work Step by Step
$$\sin^2\frac{\pi}{12}$$
*Recall the half-angle formula for sine, which is $$\sin^2\theta=\frac{1-\cos2\theta}{2}$$
Thus, $$\sin^2\frac{\pi}{12}=\frac{1-\cos\frac{\pi}{6}}{2}$$
$$\sin^2\frac{\pi}{12}=\frac{1-\frac{\sqrt3}{2}}{2}$$
$$\sin^2\frac{\pi}{12}=\frac{\frac{2-\sqrt3}{2}}{2}$$
$$\sin^2\frac{\pi}{12}=\frac{2-\sqrt3}{4}$$
