Question

sin^2(pi/8)*cos^2(pi/8)

Answer 1

$sin^2frac{pi}{8}cos^2frac{pi}{8}=(sinfrac{pi}{8}cosfrac{pi}{8})^2=(frac{1}{2}sinfrac{pi}{4})^2=\\=frac{1}{4}sin^2frac{pi}{4}=frac{1}{4}cdot(frac{1}{sqrt2})^2=frac{1}{4}cdot frac{1}{2}=frac{1}{8}$