(cos pi/8 + sin pi/8)*(cos^3 pi/8 - sin^3 pi/8) =

Решите задачу:

$(cos( \frac{\pi}{8} )+sin(\frac{\pi}{8}))*(cos^3(\frac{\pi}{8})-sin^3(\frac{\pi}{8}))= \\ =(cos( \frac{\pi}{8} )+sin(\frac{\pi}{8}))*(cos( \frac{\pi}{8} )-sin(\frac{\pi}{8}))*(cos^2( \frac{\pi}{8} )+sin^2(\frac{\pi}{8})+cos(\frac{\pi}{8})sin(\frac{\pi}{8})=$
$=(cos^2( \frac{\pi}{8} )-sin^2(\frac{\pi}{8} )) * (1+ \frac{sin( \frac{\pi}{4} )}{2} )=\\ =(cos( \frac{\pi}{4} ))*(1+ \frac{1}{2 \sqrt{2} } )= \frac{2 \sqrt{2} +1}{4}$