Answer
$$\cos^2\frac{\pi}{8}=\frac{2+\sqrt2}{4}$$
Work Step by Step
$$\cos^2\frac{\pi}{8}$$
*Recall the half-angle formula for cosine, which is $$\cos^2\theta=\frac{1+\cos2\theta}{2}$$
Thus, $$\cos^2\frac{\pi}{8}=\frac{1+\cos\frac{\pi}{4}}{2}$$
$$\cos^2\frac{\pi}{8}=\frac{1+\frac{\sqrt2}{2}}{2}$$
$$\cos^2\frac{\pi}{8}=\frac{\frac{2+\sqrt2}{2}}{2}$$
$$\cos^2\frac{\pi}{8}=\frac{2+\sqrt2}{4}$$
